During my free time I play the piano.
Also I play game, too.
My favorite hobby is playing the piano.
Because when I play the piano, I play all song that I like.
So my favorite hobby is playing the piano.

correction:
1. Let's not forget to use the possessive pronoun "my" when we are referring to something that belongs to us.

2.  "THAT" we use it as a determiner, a demonstrative pronoun and a relative pronoun.
I play all song that I like. (pointing to one of a selection)

3. Let's avoid repetitive sentences.