On the original LOZ when you bombed a Dodongo half way on their body they became stunned. Then they could be hit by a sword to give more bombs. This doesn't happen at all in ZC. In fact the Dodongo's don't drop anything ever.
They should automatically drop bombs when killed, and also they should be stunned and auto drop bombs hit the bomb explodes on the midpoint of their body. This works in the original LOZ.
I'm pretty sure this does work. At least it did pre 2.5. Actually I know it does because I used it in LQftH2.
They only drop bombs when killed with the smoke trick. If you use a super bomb for the trick they drop a super bomb. I believe this is the same in LoZ(not the super bomb obv). I don't think dodongos drop anything besides when killed with a sword.
Don't use the bomb delay quest rule in conjunction with this. It isn't impossible, but it is a lot harder to pull off.
Dodongos become stunned if the bomb explodes in their face.
Dodongos should always drop bombs in the default quests, yes. Check item dropsets otherwise.