Adventurer cards have two sets of characteristics.
When you go to cast the card (usually from your hand) you choose either to cast the creature part or the instant/sorcery part. That choice determines what spell goes on the stack. There is no ability involved.
As for your second question, you may cast the creature part of the card from exile immediately, assuming it is otherwise legal. Creature spells normally have what is called “sorcery timing”. You can cast them during your own main phase when the stack is empty. Nothing about Adventurer card rules changes this timing.
For Giant Killer
1) Is the instant considered an ability? If Prison Term is attached to it can the instant be casted?
If you attach Prison Term to Giant Killer, this means Killer is a creature, on the battlefield: with or without Prison term, it is way too late to cast the adventure part.
1) Is the instant considered an ability? If Prison Term is attached to it can the instant be casted?
2) Once it's exiled, can I cast it from exile right away or I have to wait a turn (it says "later")?
When you go to cast the card (usually from your hand) you choose either to cast the creature part or the instant/sorcery part. That choice determines what spell goes on the stack. There is no ability involved.
As for your second question, you may cast the creature part of the card from exile immediately, assuming it is otherwise legal. Creature spells normally have what is called “sorcery timing”. You can cast them during your own main phase when the stack is empty. Nothing about Adventurer card rules changes this timing.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules