Is there anything preventing a single player from drawing both of the same company tiles (both East Indies or both Levant tiles?)
There isn't a rule preventing it. Another player could (and perhaps should) draw the second tile before the first player can do so.
Also - once owned is there anyway for a player to lose a company tile?
Nope. The only tiles that can be 'lost' are the temporary tiles, such as Alliances, which are returned to the stock at the end of each War.