I've only had a brief glimpse of it, during my meal break from work. I'll tell you these things.
First is a tip. Right click on 'Borderlands' in your games list and get the cd-key from the menu for it. The pain in the arse that it is, it will be the first thing asked of you.
Now the things you wanna know.
The stash is non-transferable. No swappsies between your alts. It starts with 12 slots in a vendor type interfaces. (It's the claptrap in the tux behind the cashiers counter). The other vending machines have more slots available. At a price. I paid close to a 100 million for level 10 storage. Some forty -odd slots. Tip: buy in bulk.
I don't know if the kills count towards challenges but I can confirm the Underdome is not without some xp gains. There is a bulletin board with your first challenge already there.
There are 3 doors that I saw leading to, I'm supposing, different Arenas. Your first mission has 3 check-boxes. Maybe they correlate.
The only other thing I've noticed is a small Shrine to the 3rd Husband, Marcus.
And that's all I found out on my lunch break.
I'll find out about proficiencies when I get home.
I just want the Hat!