Those are questions that you would ask about a particular musical STYLE. In general, there are no rules about what you do with your hands at the piano. You just do whatever sounds right.

If you have a good music store in you area, you probably can find books that will teach techniques and exercises to help you improvise in a specific style or play lead sheets in a specific style. Even if you don’t know yet what style is right for you, spending some time with a book like that can help you figure it out. And meanwhile, even if you haven’t figured out what kind of music "does it for you," practicing ANY kind of music will help you out.

I myself walked into a big music store and asked, "do you have any books to teach rock piano techniques or blues piano techniques?" Almost the entire store was devoted to scores for specific classical piano and orchestral works, but the clerk lead me directly to a shelf that had a dozen or more books that fit exactly what I was asking for.

Personally, I would prefer to play a bass line with my left hand, chords with my right, and (ideally) somebody ELSE would sing the melody.
References :

Which hand do I play the chords with and then what notes would I play with the other hand. I just don’t understand how to play chords…I can read notes but I realyl want to learn chords.
but how do I know what the melody is?