Traveling for 2 months, brewing advice

Hey all, I was recently drawn to this site by my love for beer and possibly brewing beer as well, and I have a few questions.

I would really love to get started, but I only have about 24 days between now and when I have to move out of my apartment. I know that longer is typically better, but would that be enough time to brew say a hefeweisen (or any other wheat beer)?

My second question is pertaining to the topic of this post. Once I move out of my place I will be at home for about another 24 days before traveling. I was wondering if I'd be able to just brew a beer and leave it until I get back and if so which stage I would leave it in for that amount of time. Or are there maybe beers that require such a long fermentation time? I would really like to get into the hobby, but wanted to know if there was something I can do with this kind of timing. If not I will just try something when I get back, but I would love to get started on it sooner rather than later!

24 days is long enough to bottle for your first batch. Bring the bottles with you to your new place.

Same for your second question, depending on how long you'll be traveling. But if you bottle just before you leave, the beer will be fine.

I've read it generally takes about 2 weeks for homebrew to carbonate. During this phase I guess it's ok to move around right? Is it sensitive to temperature changes (say if it were to be in my car for 5 hours, would that have adverse effects?). Finally, once the beer is bottled how long should it keep and is there an ideal time to drink it/does the taste change after a certain point? Thanks for the advice, I'm getting incredibly excited!

If i Understand correncly you are moving in three weeks to your parents for three weeks before you have to travel for 8 additioal weeks?

In that case you can do just about anything. I would not do a wheat/weiss, a robust porter would IMO be perfect.
Brew now, leave in primary until you get to the P's then rack to secondary. Before you leave bottle woth priming sugar. Call your parents about a week before you get home and ask them to put a sixer in the fridge. When you get home injoy the best beer ever....