My first trip to Japan, some questions

Never been to Japan so I can't be of much help :/.
Have a fun trip! :D

Word was that nigerians and yakuza like to put drugs on drinks to then steal your stuff so avoid going to clubs at roppongi.

Don't act like a weebo so they don't think you're a weirdo I would say. Also for travling in general don't accept food from strangers. I know a dude who got drugged on the bus after accepting orange juice which was still sealed and they toot all his stuff because he was passed out.

Long-time Japan resident here. I don't live in Tokyo, but have been a few times. Japan is a big place and although people like to generalize a lot, there are many different facets and experiences just as in any country so don't get too nailed down into a "someone said it will be this way on the internet so it must apply to every single person/place in the country" perspective.

To answer your q's:

How are the weather over there by 22 to 26 March? How much cold wear should I bring?
It can be somewhat variable, like early spring in other places that have 4 seasons. Generally I'd plan for layers and a light jacket that you can put on or remove easily as necessary depending on the day. That part of the season you might be able to catch the cherry blossoms in full bloom -- might be slightly early for Tokyo area but if it's warm the next couple weeks you could be in for a real treat. A common practice for the Japanese is to enjoy a picnic & beer under the cherry blossoms in a park, termed "hanami".

What are the must-buy souvenirs?
This is really dependent on what you are into, or what your friends/family might be into. There's so many different aspects of Japan that can be appealing, you should really consider the things that you are most fascinated by and maybe concentrate on those. For example, since you are on SteamGifts you obviously have some interest in video games, and if you are spending some time in Akihabara I'm sure you'll find some really unique video game shops and could probably score some awesome vintage gear like PC-Engine or Sega Saturn/Dreamcast or PS1/2 and all the unique games that were never released outside of Japan.

What are the things that I should be aware of? Like cultural taboo and things that I should avoid doing 'cos it might offend people.
There are quite a few cultural things to be aware of -- too many to list here, so I'd just recommend googling a few lists and trying to keep those things in mind. Non-Japanese actually tend to get a bit more of a break as the Japanese will usually just think they don't know any better and will cut them some slack, but as an ethnically Asian non-native myself I sometimes draw some glances unless I've made it patently obvious that I'm non-native in some way (like speaking English or broken Japanese). Also, you probably shouldn't sweat it too much, if you do something extremely unbecoming it will be obvious that you aren't Japanese and people will generally cut you some slack since it's obvious you aren't doing it on purpose.

How hard/easy it is for foreigner who does not understand any Japanese to navigate over there?
Tokyo is generally pretty English-friendly, and it's not usually that hard to find someone who would be happy to assist you in some way even if they don't speak English very well. If you have GPS and can input map coordinate into google maps it would probably help you navigate a lot and you'll be able to see more places more easily.

Any good translator/navigation apps that are very useful that I should install to my Android phone before I go there?
My dictionary app of choice is "imiwa?" on iPhone, not sure if there is an Android version or not but something similar should be helpful for basic word lookups. I think something quick and with speech recognition like google translate would be handy if you need to ask someone who has no English ability about something quickly -- the translations are often pretty bad but it's better than nothing and opens some form of dialogue if you feel horrendously lost (though as long as you just keep a fun/light atmosphere about it all people will generally be pretty happy to help).

I heard it is super safe in Tokyo, as in it's a crime-free country. Is it true?
It's not crime-free, but the violent crime rates are very low compared to most other countries. Put this way, there were neighborhoods in the USA I've lived where I did not feel comfortable walking around alone at night at all and would always keep my wits about me because the possibility of getting mugged/shot/robbed is always present -- there's nowhere in Japan in my 12 years of living here that made me feel even remotely like that. Sometimes non-Japanese people can get into trouble in the club/night district areas, but usually that's only if they are drunk or kinda looking to get into some trouble. If you just keep a low-normal profile and don't try to start any shit or do something illegal you will generally be left alone.

It's almost 20 degrees right now in Tokyo, which is exceptionally warm comparing to the weather we had so far. Usually it gets pretty warm at the end of March (or at least what I consider "warm", around 20 Celsius), but in the past year a there have been exceptions and you would need a winter coat even at the start of April. Probably you should wait and check the weather forecast a couple days before leaving, it might be the best thing.

As for something you should try not to do: talking loudly or speaking on the phone on the train. It took a while for me because in my home country trains are the loudest places you can find, but after a while you get used to silent commuting and you start to appreciate it.
As someone said above, it's not really necessary that you act just like a Japanese person - people can see you're not so they will forgive you most inappropriate behaviour. You should try not to make people around you feel uneasy though, and the best thing to do this is look around you and imitate people you see: if everyone is queuing in two lines to catch the train, do as they do. If everyone takes off their shoes to enter some place, do as they do. And so on. But really, don't worry too much:)

With the premise that criminal it is everywhere, I would say Tokyo is a really safe place for a tourist. No one will try to steal anything from you and no one will lure you into paying a shitload of money when you really shouldn't (except for some dangerous looking guys in Kabukicho what will lure you into going to their pubs to get all the ladies and will make you pay A LOT for it in the end). Of course there is no country of city that is 100% safe, so use always your judgement and you'll be okay!

Most of Japanese people have studied English but they're not very confident when it comes to speaking. People in shops or restaurant though will often try their best to help you! I suggest preparing a list of useful Japanese words and sentences just in case every other way of communicating goes wrong, but you shouldn't have any big problem.

If there's anything else you'd like to ask just add me on Steam, I'm always glad to help newcomers in Tokyo (which by the way is a good place to visit and for some people LIKE ME an even better place to live in!)

Wow at some of the responses I get!
Seems like I definitely need to learn some basic Japanese phrases before I go.

' cultural taboo and things that I should avoid doing 'cos it might offend people." https://www.youtube.com/watch?v=HYMBkrxeVvY

Apparently many useful tips for tourists are already posted above so I just recommend Asakusa for your sightseeing plan. There are full of Japanese traditional stuff you can enjoy even if you don't know Japanese language. Store staffs and signs are much more English friendly than in the other places in Tokyo (although Tokyo is relatively English friendly than the other cities in Japan) since the place attracts many tourists from all over the world. Kaminarimon will be something you can remember afterwards as well as some shinto shrines. You can go there in the daytime but in the evening the atmosphere is getting better. I don't think you have to always worry about your back and pockets in the evening as people already pointed out.

Aww, I want to travel one day too. :(

Tell FIlthyFrank I said, "Hi.".

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View attached image.

How are the weather over there by 22 to 26 March? How much cold wear should I bring?
-Weather should be pretty close to the US, but if you're climbing Mt. Fuji, you'll want to bring something for the cold
What are the must-buy souvenirs?
-Whatever fits your interests. There's plenty of historic themed things, Darumas are pretty common souvenirs, I always like sharing snacks that can't be found in your home country, and of course plenty of anime stuff (Akihabara is kinda known as the place to go for that)
What are the things that I should be aware of? Like cultural taboo and things that I should avoid doing 'cos it might offend people.
-If you can learn a bit of the language that'd be good. Stand in line, reciprocate bows, take your shoes off if you enter a home, that kind of thing. You can get by a lot just following along social cues you see. If you start to feel under the weather, it's courtesy to wear a mask to prevent spreading your germs and you may be asked to wear one if you start coughing.
How hard/easy it is for foreigner who does not understand any Japanese to navigate over there?
-Airports should have English, but trains and busses are the way to get around in Japan, and they mostly just have Japanese. If you know enough to ask for directions, you should be able to find someone who can help even if you can't read. Try to memorize a couple of common phrases, and if all else fails, most people study English in high school, so you may find someone who still remembers some. Additionally, some words are "stolen" from the English language.I guess what I'm saying is making hand gestures and grunting is better than nothing XD
Any good translator/navigation apps that are very useful that I should install to my Android phone before I go there?
-No recommendations off the top of my head here, sorry. Anything with a Japanese-English dictionary is enough if you already have some understanding of the language, Japanese-English doesn't have a ton of great translators yet because they don't share the same root language, making it more difficult
I heard it is super safe in Tokyo, as in it's a crime-free country. Is it true?
Not 100% crime free of course, but it's very safe. If you use about the same level of caution as in your home country, you should be fine. You're likely to have more problems from the language barrier than from crime

Enjoy your trip!

funnily enough usually foreigners have to fear the least the yakuzas, they wont harm you in any shape or form

to quote from yahoo answers

"Tourists are in no danger at all from Yakuza.
It is a crime organization but it does not involve itself with harassing foreign tourists.

For a foreigner to be afraid of Yakuza would be like a Japanese tourist being afraid of bank robbers when visiting the US.

Crime is simply not a problem in Japan.
Street crime, organized crime - you name it. Not a problem."

simply put: unless you are explicitly looking for troubles (which I assume you wont), you will be fine

stay way from the Fukushima area and if you want to blend in, kill as many whales and dolphins as possibru

I have created some GAs before I depart tomorrow. Trains are too troublesome, so I will just list them all. Good luck!