So do you need a studio to be a successful musician?

Absolutely not.

By no means do you need a studio to be a successful musician. It just depends on what you want to do. If you want to be a musician (meaning someone who plays an instrument), you just need a place to store your instruments and a place to practice. However, if you want to record your music, you probably need some sort of setup. This is just to be more organized. If you think that you can pull off recording your whole song while sitting on your bed, by all means go for it. If you want more of a professional setup, you should probably get a few things. If you want to setup your own studio, visit the how to build a studio page. It will give you all of the materials that you need, and how to utilize your space effectively.