The correct answers are A squirrel stole my homework, and it ran up a giant oak tree. and I chased the furry thief for ten minutes but couldn't catch it.

Use a comma before a coordinating conjunction (and, but, or, so) ONLY when it joins two complete, independent clauses (sentences that could stand alone).

I chased the furry thief for ten minutes but couldn't catch it. is correct without a comma because "couldn't catch it" is not a complete sentence (it has no subject).

I tried to bribe it with a peanut, but failed miserably. is incorrect because it uses a comma before a compound verb.

The squirrel looked at me and, it just laughed. places the comma on the wrong side of the conjunction.