1) Can Unity be used for online games: Yes of course, many online games were built in Unity.
2) Can Unity be used for an MMO: depends on your definition, but AFAIK there are also games with persistent worlds built with Unity.
3) Does Unity have to have a one player mode: No, of course not. Unity is a pretty open multipurpose engine, there is little you cannot do, some things are just less easy to do than others.
But:
1) Does Unity do Networking out of the box: No, not really. You get some networking functionality, but if you really want scalable networking, you need to add a lot or use 3rd party implementations.
2) Is Unity an MMO engine out of the box: almost no engine out there is "an MMO engine" out of the box (I'm getting to that further below). Unity is not much different. Use for you client whatever you want, the server part often needs a very custom solution.
3) Is it a good idea to even talk about creating MMO's when you got into game dev "recently": No, totally not. Chances are good you have little grasp on the technical complexity involved with persistent worlds, and you try to run before you can walk. Also, MMO's are usually consuming 10+ million $ in cash just to develop, not talking about servers and maintenance to keep it running now. You really have enough money lying around for that?
About the MMO Engines: I know of 2 that where built for exactly that purpose...
- Bigworld: You could license the engine until like 3 years ago, then it was bought by Wargaming and is now proprietary for their own MMO games.
- Hero Engine: http://www.heroengine.com/ ... a lot of bells and whistles for MMO development. How good and scalable it is after the marketing blurb, I don't know.
Quick word of advice: either keep it to modding existing MMO's, or drop the MMO idea for good (until you get filthy rich), and save the multiplayer for later. Start more modest with singleplayer games, very simple one at first, until you get a better idea just how much work and money is involved in game dev. Try to finish multiple projects, each a little bit more complex than the last.
Then, when you feel confident you can build a game, try your hand at a multiplayer one.