Can your Familiar make attacks such as bite?
Yes. But since your flying squirrel (like most familiars) is Tiny, it has to enter an enemy's square to attack them, rather than being able to attack from an adjacent square. That will get the enemy a couple of attacks of opportunity on it. So be careful sending it into battle. (Also its bite won't do very much damage.)
Can you make touch spell attacks though your Familiar? Example: My squirrel run's up behind a thief and jumps on to his back, then I cast Shocking Grasp, (Touch delivers 1d6/level electricity damage (max 5d6).) would that be or could that be delivered though my Familiar?
Yes, except (a) you need to be 3rd level for your familiar to deliver touch spells and (b) you have to cast first, then send your familiar out, as per
Deliver Touch Spells (Su): If the master is 3rd level or higher, a familiar can deliver touch spells for him. If the master and the familiar are in contact at the time the master casts a touch spell, he can designate his familiar as the "toucher." The familiar can then deliver the touch spell just as the master would. As usual, if the master casts another spell before the touch is delivered, the touch spell dissipates.
Again, your familiar is Tiny and fragile, so casting buff spells on your friends this way is safer for it than zapping your enemies.
Yes, a Tiny creature gets a +2 to AC.
When you pick an arcane school you don't actually give up the other two schools you select, they just become your opposition schools, which makes it harder (but still possible) to cast spells from them:
A wizard that chooses to specialize in one school of magic must select two other schools as his opposition schools, representing knowledge sacrificed in one area of arcane lore to gain mastery in another. A wizard who prepares spells from his opposition schools must use two spell slots of that level to prepare the spell. For example, a wizard with evocation as an opposition school must expend two of his available 3rd-level spell slots to prepare a fireball. In addition, a specialist takes a –4 penalty on any skill checks made when crafting a magic item that has a spell from one of his opposition schools as a prerequisite. A universalist wizard can prepare spells from any school without restriction.