I supposed that if I'm the first one to offer my shares they will be bought first if me and someone else offer shares at the exact same price. Right?
You have to check the NYSE ARCA website to see if they offer time and price priority. I expect they do but they might allow crosses at your price.
Well it may be reviewed by your brokerage compliance department (especially for short sale orders) before it goes live. Other than that I don't think anyone else has access to your order before it goes live to the public.
Oddly enough, I saw this for the first time today (although, during market hours). Was shorting SNAP.