About steam offline mode

1. Not sure, never check. Most likely no.
2. Yes, it will be uploaded for stats later when you're online on that machine.

1-dont now
2-yes

Playtime does not increase while in offline mode.

1- I had problems with it. I could say no.
2-yes
anyway, the main point is to enjoy the game. try not to care about the play time steam shows. If U can get online while playing, do it. offline mode is good only when it's not possible to get online.

About those saying "yes" to achievements. Technically yes, though Steam is notorious for improperly uploading earned achievements, if at all, when earned offline. They still pop as earned, but if anything happens during the upload they may not register (and, in the case of some games, require a save wipe or total reinstall to earn again). Just a warning.

From my experience it varies by game. I played one game for like 6 hours or so and I didn't realize my internet connection went haywire. It still shows up as 2.5 hours played even though i played roughly 10 hrs.
On the other hand I once played deliberately in offline mode and the game time updated correctly after I went online again. It also updated all the achievements at once. Didn't happen with the other game at all.

tl;dr: YMMV

Not every game gives you achievements while offline mode

1- Only offline. To me, it didn't. I have like thirty-something hours in broken sword 2 but, if you check, I never played it (apparently).
2- Yes once you are connected online again, I think

As a 99% of time offline player, I can tell you than many games have broken achievements in offline mode. And there's nothing to do to fix that...

1. In my experience, no. It only records your gameplay during the session when you're offline only. Once you exit from Steam, the playtime will be lost.

2. Some games may update the achievement earned during offline gameplay session once you log into Steam, provided you've launched the game with an internet connection before. However, there are also several games that don't update the achievement at all, making earning achievements offline unreliable.

1. You're play-time hours do not increase while playing offline.
2. I did some testing on this a while ago, and unless something has changed since then, this is what I found. If Steam is offline and you are still connected to the internet, Steam still "phones home," so achievements still register, and you will even get Steam client update notices. If you have Steam in offline mode and have no internet connection, they don't register.

1 - Does the playtime increase for that game?
most games dont
2 - Can I still get achievements?
there are a few games that wont let you get achievements unless you are online, Lego hobbit is one of them