1. You must have an Advance Parole before you leave united states. It will usually take around 3 months but apply it before 4 months of travel. You can request for expedite processing too.

2. Regarding TPS renewal, it has not been decided yet but if TPS is renewed to Nepal, then there will be 2 months time for renewal which will be most probably from Mid October to end of December 2016.

3. If you have other valid visa status such as F1-H1 with visa stamped along with TPS, you can travel on those visa too but TPS might not get renewed since you do not take Advance Parole.

4. If you take Advance Parole and travel to Nepal, you will be entered into Parolee status, so it might affect your current H1b visa and your green card processing. Your employer will file your Green card based on employment based which is H1b but when you use an Advance Parole you will be entered into Parole status.

Based on your situation, you have to make a judgmental decision whether to travel on AP or regular visa. The bottom line is if you travel it is difficult to maintain both H1 and TPS, you have to sacrifice one.

Disclaimer:The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.