1) Will the alligator swallow the guy face up or down?
Probably face up - it would go down more smoothly.
2) How long will it take the Alligator to swallow the guy’s body?
About 15 minutes.
3) Would the alligator be able to tell from the taste that the meal it was eating was male or female?
No. An alligator's taste buds aren't that developed.
4) Would it notice a difference in what it was eating in the swim trunks from the rest of the meal?
The trunks would give it a different texture as it was swallowed. The alligator wouldn't like that texture, but since the trunks would be wet, it would be easy for him to simply swallow. As for what was inside, to an alligator, it would just be more meat.
5) Once it has swallowed the guy Hole and it is basking in the sun to start digesting the meal. What parts of the guy will be digested first?
Muslce and fat would be easiest to digest and would go first. That would include the private parts, which are mostly fatty tissue.
6) What happen to the guys swim trunks and what’s in them?
What's in them would be quickly digested. The trunks themselves would deteriorate from the stomach acids, but would be passed out in the gator's droppings.
7) How long will it take the Alligator to digest the guy’s body?
A few days.
8) What will be left after digestion is completed, how will it get rid of anything it can`t digest.
It will be passed out in feces. Hair and the swim trunks would be visible in the droppings.