combat damage question x2

[TheWhiteDragon]

This is a dumb question, and I believe I know the answer, but I'll ask anyway:

I have a goblin lackey and a goblin chieftain in play (both 2/2 haste).  My opponent has a 1/1 delver of secrets in play.  I swing with both and he flashes in snapcaster to block the chieftain, then blocks the 2/2 lackey with his 1/1 delver.  After combat damage is resolved, the chieftain dies and my lackey shrinks to a 1/1, which then dies because it has 1 damage to it...correct?

Less dumb, but still dumb:

I attack with a warren instigator and my opponent blocks with a 1/1 delver.  The first strike damage kills the delver.  Is the regular second strike just a whiff in mid air since the blocker is dead, or does the instigator connect with the opponent now that there is no more blocker?

[Thecheese]

Answer to first situation is yes you have it correct.

Answer to second is no damage gets through because he is blocked. Even though he has double strike. He would need trample for it to matter