To answer your questions directly:
You can only create a character starting on Normal difficulty. You'll have to defeat all 4 act bosses and complete the Prime Evil quest on Normal difficulty to go to Nightmare and play with your friend who is on Nightmare, and you'll have to redo this process for any character you create. This follows for other difficulties as well. Edit: There are now level restrictions: you must be 25 to advance to Nightmare, 50 to advance to Hell, and 60 to advance to Inferno.
You must be online when playing Diablo 3, so you can join your friends whenever you want. You can join a friend's game without invitation unless it is private. If it is private, message them asking for an invite.
If your friend just buys the game you can join him in his quests, but he cannot join you until he has unlocked the difficulty you are playing on.
One important thing to note is that the only restriction for friend joining you is that they have unlocked the difficulty you are playing on. Unlocking quests doesn't matter; only unlocking the difficulty does.
So if you want your friend to play with you, change your quest to a quest on their difficulty. Note that this doesn't mess up your save file or anything; you will be able to return to your previous quest and difficulty after you've played with your friend.
First click the Change Quest button in the main menu (notice I am currently on Hell difficulty):
Then select Normal Difficulty from the drop list:
And finally select the any quest (here I select Prime Evil) and click the Select Quest button:
Note the warning: the only drawback to this is you lose all progress for your current quest. So finish up what you were doing before switching your quests!
After clicking OK, then you should notice your current quest change in the main menu:
And now when you start the game your friend can join you.
I've done this with my friend to skip the Butcher on Hell difficulty, mostly because I wasn't geared to fight him toe-to-toe. Proof is here that joining your friends can help you skip bosses (I skipped Butcher but killed Belial):
However, to advance to the next difficulty you will have to defeat all four act bosses.
If players are within 4 levels of each other, experience is worth 100%. Starting at 5+ levels apart, experience decreases by 10% each level until it reaches 10+ levels apart, it then decreases by 95%.
Example: a level 1 being boosted by a level 60 will still receive 5% XP per monster kill.
However, if you legitimately kill monsters in a more difficult act with friends your own level (or solo) you receive the full amount of XP.
No solid citations yet, sorry.
Best Answer
The Stash is shared between all of your (non-hardcore) characters. Capacity upgrades are shared as well.
That said, early on stash capacity upgrades are an extremely inefficient use of your gold. You're better off making an additional character to act as a mule to hold on to that cool axe you want to give to your barbarian someday - it's slightly inconvenient to move stuff around, but compared to the inconvenience of raising 10,000 gold at this point in the game, it's definitely the better choice.