Hi Varun,
1. You generally shouldn't leave any gaps in your address history or personal history. As such, yes, I would recommend that you account for even these short unemployment periods in the personal history.
2. You only need to account for work experience for which you're claiming points in your work history (and it should be under personal history as well, which is why the application automatically puts it there). As long as you're not claiming points for them though, any other work experience should only be stated under personal history. So, yes, you're on track here.