If an opponent unsummons my Goblin, does it spoil my Goblin Grenade?
It is impossible for your opponent to unsummon your Goblin after you have chosen it to be the grenade victim.

When you cast a spell, announcing the spell, choosing its targets and modes, and finally paying its costs (and yes some other more fiddly things), is all a single action that you take at once.  Other players do not get priority to interrupt you in the middle.

Because sacrificing the goblin is part of the cost of the spell, it is part of that one big action and other people can't jump in the middle to do something.  By the time your opponent gets priority again after you have chosen the goblin, it is already in the graveyard.