Marowak

When I try to attack, does Marowak's "Bodyguard" Ability prevent me from having to flip a coin if my active Pokemon was attacked last turn with Silicobra's "Sand Attack"?

The effect of Sand Attack is on your Pokemon that was attacked, not on you. So, Bodyguard does not prevent you from having to flip a coin to see if the attack goes through

Does Marowak's "Bodyguard" Ability prevent me from revealing my hand from an opponent's Trevenant's "Poltergeist" attack?

Yes, it does.

If I used Volcanion EX's "Volcanic Heat" attack last turn, then on this turn I play Marowak and use its "Bodyguard" ability that says to "remove any existing effects", does that mean I can use Volcanion EX's "Volcanic Heat" attack on this turn?

Sorry, but no. You can only remove effects that were done by your opponent's Pokemon, not effects done by your own Pokemon.

If Marowak's "Bodyguard" ability is in effect, preventing the effects of attacks on me and my hand, does Greninja's "Shadow Stitching" attack turn off abilities of Pokemon in my hand or not?

Shadow Stitching turns off the Bodyguard ability, so until the end of your next turn none of your Pokemon will have Abilities.