I have a few questions I don't know the answers too, because I have not yet reach the appropriate level or skill to learn the ability.
Also I'm planning my character ahead.
So here I go:

• If I would use Invisibility (from the Illusion school) for pickpocketing a enemy, would that break the Invisibility when I remove the item from the enemy, so they would detect me?
  
• Is it possible to configure the game somehow that those dead people you left behind in caves or out in the world, will stay there as you left them? Because they don't, they vanish into thin air after short time.
  
• If you gain the Illusion perk that make spells in all school silence to others, will that make it possible to assassinate\murder somebody with a Firebolt for example (1 shot) in a room with a closed door but still in the same house or will everyone know?
  
• And last question, the perk on Restoration tree that says you regenerate 50% mana, it's the perk to the right, second one. 1/2 25% mana and then I believe 2/2 is 50% mana. Well, do this perk effect mana regeneration while you are in combat?

Please, no spoilers! Yes or no and informartion that contain no spoilers are welcomed.

1. Invisibility is removed as soon as you take an action. It is really something to enhance Sneak rather than replace it.

2. Believe me, you want the corpses to dissapear, save files are getting big enough already. So, no, the corpses should go away after 72 hours. The game has to keep track of every corpse otherwise.

3. I think the Silence spell stops others from casting magic, at least that is what is did in past games.

4. Mana regenerates slower in battle, not being a magic user, I can not comment on the subtleties.

The perk he's referring to is the one that makes your spellcasting undetectable.

However, I believe that with offensive magic, the end explosion makes too much noise - It leaves your hand silently, but then goes KABOOM!

That's kind of silly if the spell effect still makes noise.

I guess it could work like an Arrow where the NPCs investigate where the arrow lands rather than where it came from if your sneaking.

Thanks for the replies, but that leaves me with another question.

• So if the Illusion perk only silence the spell casting, charing up the spell. What kind of spell could you use to take advantage of that perk to assassinate one for the Dark Brotherhood for instance as pure mage while roleplaying a stealthy mage that never gets detected. Without having to be "forced" to use a real weapon like dagger, bow. (?)
  
• (Edited in) and I almost forgot.. Will corpses dissapear in your own house that you bought if you slay your wife or something and hides the body in the basemant?

1. Assassinating as a pure mage isn't going to happen in this game, unless you have the difficulty way down to where you could have one shotted them silent or not. In other words, there aren't any damage multipliers for casting a spell undetected. The silent casting perk works well with other illusion magic such as: frenzy, calm and fear. It also enhances sneak because once the spell hits an enemy and if it makes noise they will search for you and have a hard time finding you if your sneak is high enough. You can use it to cast summons on top of your enemy and fire away with destruction spells, and if any enemies are left, again if your sneak is high enough, they will have a hard time finding you. Rinse and repeat.

As for the spell to kill an enemy undetected? Depends on their level and your difficulty level. Maybe a dual casted incinerate? Again, no sneak damage multipliers though.

2. All corpses despawn after 72 hours, some sooner.

Edit: By assassinating I meant killing an enemy with one hit / shot as done by 30x dagger damage and 3x bow damage. I just don't think destruction can match that damage. Keep a lot of fortify destruction potions around maybe.

Magic regeneration rate, normally is 100%. In combat, its 100/3 %, 33%, a third of what it is normally. If you have both restoration perks, you will have 150% normally, so 150/3 % in battle, which is 50%.