In both cases "He and I" is formally correct. "Me and him" is a common and widely tolerated conversational form that may, especially for #2, seem less pedantic. Similarly for "Him and me", though that seems slightly less natural to me.
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gabbnoniWho baked the cake?Just an observation:
-He and I or He and me
2.- Who are the guys in the picture?
He and I or He and me?
keepsmilingAbout your third question
The manner in which the question is asked, we reply in the same manner like
"who are the guys in the picture?
There is nothing wrong in replying like
You and she are the guys in the picture.
Same thing can be pointed like you have said
the guys in the picture are y