Just to follow on a little more from Chris' reply.
> 1. Is there a way to see whether im ranking for any keyword if I don't know the keyword, in other words, how do I know if I rank for any keyword?
By looking at your Google Analytics search referrals you cannot tell where you are ranking but by the fact that you have had a referral from a search engine means you must have been ranking reasonably well for a search phrase in order to get a click through.
Please note though that if pulling this information from your Google Analytics, for the last year or so Google has gradually been returning more and more "(not provided)" results. These of course don't tell you what people were searching for. Recently, Google has pulled search referral data altogether. Now you can only see if you have had a referral from Google and not what the search phrase was. So only by looking at historic data for Google search referrals will you get the info you want. But you can still get that data from Bing and Yahoo referrals.
> 2. I added a list of keywords to Moz but it says I don't rank on first 50 results. So how do I know if I'm ranking for anything at all?
Yes, Chris it right, but if below 50 then it maybe worth re-examining the phrases you are targeting to see how competitive they are (as your 3 point below) before spending lots of time trying to push them up the rankings. Your time may be better spent looking for longer tail searches that you can pick up some traffic from.
> 3. Ive heard of keyword competition, could you please guide me on how to actually do a competition analysis?
Have a look at this help page on the Moz Keyword Difficulty tool. That should give you a good kickstart to understanding more about it.
Peter