Someone familiarize me with keys trading

I think the first and most important thing is - know who you're trading with! It's easy to pretend to be someone else, so when you go and complain, you complain to the wrong guy. Don't trust links to profiles, find them yourself. Make sure the steamtrades profile is the same profile you're friending on Steam and chatting with.

Regarding the price - if you're happy and the other guy is happy, all is good. If both you and the other guy is trying to make a profit, the trade is not gonna happen :)

I usually use Barter, https://barter.vg/, a website, to assist in making matches. There you can 'match' with your tradeables and someone's wishlist and vice versa. They keep stats so you can easily see and check how many trades they've completed on the site, how many failed, and you can even check other's ratings on the traders. It's worked really well for me.
They also show which games have been given for free, bundled, and lowest ever price.

1TF-Key is worth ~2€ atm.

... are keys commonly accepted for trades or rather nah?
Yes

... how do I know the game's keys value?
you can check greymarket prices like g2a, kinguin. rule of thumb: if the price is okay for you that's the value

... I assume it's commonly more beneficial to trade the received keys for another game than reselling it on Steam since I lose the value due to fees? (Or whatever else am I supposed to do with them /o\ )

YES. Reason why people use these keys (or csgo keys)

1. Keys are like stocks with some pricechanges
2. people trade keys for skins from csgo and sell them later for real money
3. people sell keys on market and buy games from steam (and sell them for other games, real money...)
4. people use keys as hidden reserves

Important items/values:

TF 2 keys and CSGO (non-hydra) keys are the most widely accepted currencies. TF2 keys are worth around $1.80, and CSGO keys are worth $2.00.
CSGO has a lot of different keys, but for trading purposes they're all the same EXCEPT Hydra keys (those were originally priced differently, but it looks like that might have been fixed by now?)
Always specify whether you're trading CSGO or TF2 keys, as there is a noticeable difference in value

Next up is a Mann Ticket. That's worth around $1.00 and is worth half a key
The prices for tickets and keys are set by valve and are therefore very stable.

A Sack of Gems is the next item. The value fluctuates, but right now it's worth around $0.40, so not quite half a ticket. Each trader values SoGs differently, and trading SoGs for Keys especially depends on who you're dealing with.

Lastly, there's Ref and Scrap. TF2 allows you to turn items into scrap metal, and combine scrap metal into refined metal. These are just about worthless. Scrap is $0.01 and Ref is around $0.10. Most traders don't even bother with these.

In addition, sometimes people will try to trade cards or items. The value of these varies wildly. Most cards are only worth $0.01, though some rare cards are worth a lot more. Skins and Hats can be worth hundreds of dollars. For now, steer clear of these. Unless you know what you're doing, you're gonna have a hard time figuring out fair value for these. Let the other person worry about converting items into standardized currency (i.e. keys)