Can I get a rule check on when the Uniqueness of an equipment is checked?
Example;

Vic Stone @ Cyborg Human Machine DOR-054
Boost X: When Vic Stone comes into play, search your deck for an equipment card with a cost of X or less and equip it to Vic Stone. Shuffle your deck.

If you say had Fate Equipment in play and use an ability such as his, can you have an extra piece of Fate Equipment is play, or any other unique equipment for that matter?

Anytime equipment is attached to a character, uniqueness is checked. You can't bypass uniqueness this way.