Current Status: H1-B, Concurrent processing (140 & 485). have EAD,
advanced parole.

Given my current status I am about to start working in an office in
another country (same employer) for several months (with frequent
visits, about once in 2 months or so to the US) while maintaining a
house/address in the US and paying US taxes, etc.

By doing this am I jeopardizing my Green Card filing?

Also I haven't activated my EAD. I have nearly 1 year remaining on my
H1-B. Should I be using my H1 for trave or should I used Advanced
parole. If using Advanced Parole any issues ??