Only the 2nd looks correct to me...

Unless on the third sentence you didn't mean to add "so" in there....i.e. you could say "I spend my time on doing something" (vs. "so something" as you have listed above). If that's what you meant, then that is correct also, but agree with Dean it's a little awkward with these specific words and probably most words you might stick in its place...i.e.:

I spend my time doing chores.

I spend my time on doing chores.

I think both are correct, potentially, but the first sentence is much better.

First sentence is not good, very unnatural.

Second sentence is very natural and would be my preference.

Third sentence is correct, but sounds a bit strange.

Typically you would use use past tense instead of present, unless you are talking about doing something right now. I spent my time doing something.