About the portal to Omega Sector in Nautilus Port...

The ticket is given to you via some low-level quests. I don't know if you can get more at this point, but in the beginning, you could get one repeatedly after a certain amount of time passed, so multiple copies could exist on one character. It seems to me like the quest was meant to be repeatable, but due to a glitch, you could get the ticket without doing the requirements. It is probably fixed by now.

Ticket is consumed upon usage.

Maybe I should stop posting in red. >_>