To prepare for the Dawnguard DLC I want to improve my mage character's skills.

1) What is the highest 'magicka regenerate' you can have? What items give you the score? I'm currently about 337 for 'magicka regenerate'

2) Is it possible to 'fortify destruction' on items/apparel/equipment to the extent that it costs 0 magicka to cast destruction spells? If so, how do you get it? I have 100 for destruction and all the perks.

Any other tips for quick ways to level up particular skills? I have destruction, alteration, illusion, alchemy, speech, enchanting all at 100. Smithing 80, conjuration 62 and the rest are all very low (under 50)

Like, how do I improve sneak? I was in a dungeon and a wolf was in a cage. It had a little red dot so I thought "I will sneak about to raise the sneak stat", and although I sneaked the stat didn't rise.

Lastly, I might spend the week before the Dawnguard DLC comes out having fun being a vampire. What is the easiest way to become a vampire? Could being a vampire have any bugs/cause problems with playing Dawnguard DLC for the first time? How do you cure yourself of vampirism after you have been a fully fledged vampire for a long time?

1) It can go as high as you can enchant
2) Grinding
3) Get attacked by a vampire and contract their disease

1) Not sure. It's not capped at 85% like the Resistances are, so I guess that it'll be just as high as you can get it.

2) Yes. My Mage Ashur has his Destruction spells costing him 0 Magicka to use, and I did it without the restoration glitch. I got a bunch of the different types of Enchanter's potions (11 total potions spread across all of the different types) and Enchanted a Circlet and a Necklace with Fortify Destruction, both at 29%. Then I have the Master Robes of Destruction and the Necromage Perk (Restoration) active.

If there's a red dot, then it's an active enemy and will lower the rate at which your Sneak skill rises (even if you are still hidden). Wolves have crap for a stat to detect you, try using Sneak and following guards on patrol. It'll rise faster. Or Sneak back and forth in front of a sleeping Draugr Deathlord. The higher the enemy's ability to detect you (i.e. the tougher enemies), the faster your Sneak score will rise).

Fastest way to become a vampire is Haemar's Shame, IMO. The second enemy in is a weak type of Vampire. Get said Vampire's attention and let them hit you with their Vampiric Drain. Every time they hit you with it there's a 10% chance that you'll be infected with Sanguinare Vampiris, so keep an eye on the upper left of your screen for the infection notice. If it doesn't pop, duck back into the tunnel to put some rock between you and the Vampire, this breaks the Drain effect. Then, come right back out and the Vampire will hit you with it again, giving you another 10% chance. Wash, rinse, repeat until you are infected, then kill the Vamp and leave the cave (unless you want to clear the place). Three days later, poof. Vampire.

The cure lies in Morthal. I can't spoil every surprise for you. lol