What happens if my Fizz, which is the target for my Star Crossed, gets removed from board at Reaction speed prior to Star Crossed completion? Does the spell activate anyway and my opponent's unit goes to hand?

Yes — the enemy unit still goes to hand. Star-Crossed doesn't fizzle when one target is removed; it resolves as much as possible and only the instruction affecting the now-invalid target is ignored (Rule 359.3.e.5, 359.3.e.8; FAQ #10311, #10736).

So if Fizz is recalled, killed, or otherwise leaves the board before Star-Crossed resolves, the friendly half of the instruction is ignored — but the enemy unit remains a valid target and is still returned to its owner's hand. The only way the whole spell fails is if both targets are gone.