Do we need a comma there?

I finished my homework, and I went out for dinner.

->I finished my homework, going out for dinner.

I watched TV while I ate some snacks.

1) I watched TV eating some snacks.

2) I watched TV, eating some snacks.

The original sentence with while clause has no comma, and then when it becomes a participle construction, is a comma needed or not?

What do you native English speakers think?

Thank you so much as usual in advance.