Do I need to trademark/copyright my game or is it already protected by Unity?

I am very new to Unity and game design in general, and I have a few questions.

I am building a 3D MMO tank game right now with Unity Free (I will soon upgrade to Pro when I can increase my budget), and I am curious on whether I need to register my game for a copyright license, and a trademark license in the USA before I publish it. I do plan on selling things in this game.

1. Does Unity handle all the legal stuff since I am a member?

2. If I post my game on the Unity website, is it legally protected since a Unity product was involved?

3. Do I need to apply for a trademark and copyright license before I publish my game, or does Unity take care of that for me since I am using their product?

4. Is my studio name (DOLJMAA Games) protected right now or do I need to apply for a trademark and copy right license?

5. In short, do I need to handle the "legal stuff", or does Unity handle that for me, and all I have to do is create and publish my game?

Thank you for your time!