Can I use Act of Aggression to steal their attacking creature and block with it?
Yes, that's fine.  You would play the spell during the declare attackers step, after attackers are declared, but before proceeding to the declare blockers step.  Then you are free to declare it as a blocker.  If you wait for your declare blockers step, it's too late to block with the creature.

The ordering is:


Declare Attackers Starts: 
Turn Based Action - Attackers are declared
Players get Priority &lt;- Cast Spell Now! 
Declare Blockers Starts: 
Turn Based Action - Blockers are declared 
Players get Priority &lt;- Too late
to use as blocker if cast now!


Any time a creature changes controllers, it is automatically removed from combat, so it will no longer be considered attacking you (or attacking/blocking at all if it previously was).