Can I play two different characters at the same time? Any limitations against this?
Yes, there are limitations, you can't log in twice on the same account on the server. You'd need 2 accounts and a capable machine, or 2nd pc. You can be on tribble and holodeck at the same time with one account though.
I've seen it done on F2P games so that a player can transfer stuff and/or cash from one character to another without going via the mail. In STO you can't transfer EC via mail so you need a third party to hold it while you change accounts. However, there are other ways of doing it without trading it to a third party (the exchange for example, put some cheapo common item up for sale for 500K or 1 million EC and have your rich character buy it).