Form I-130

While an approved I-140 with an employer offers some benefits, an EB-2 NIW grants portability - you can keep your green card across job changes in your field. It also allows extending your H-1B past the 6-year limit and enables your spouse to work and travel with you.  For those with backlogged priority dates (e.g., India), NIW can help with I-130 petitions in specific situations. If your I-140 is approved already, the main advantage of NIW becomes self-sponsorship.  Finally, you can renew your H-1B visa stamp before expiry, though consulate lead times (like four months) might apply.

If your green card application is family-based, such as through your spouse, and you have student status, it could potentially become a problem if you travel. In your case, I would suggest traveling only after you obtain either an H-1B visa stamping or Advanced Parole.

A. Certainly, there is absolutely no problem with that; a green card can be in process, and an H-1B can be filed.

B. No. The pending green card application should not hamper or impede the grant of an H-1B visa because the H-1B is a dual intent visa.