B1/B2 query while GC is filed

Hi guys: all your suggestions or inputs in the following case will be highly appreciated. This is for my family member.

  • Applied for green card and travel permit in May 2020
  • got travel permit(b1/b2) in March 2021 which is valid for a year; difficult to apply for another one as process takes too long
  • still awaiting for green card

Two questions

  • can She travel back to India before green card is issued Incase she enters US in end of February and as b1/b2 also will expire by then.
  • why is green card taking sooo long? People who applied after her got it
    FYI - She submitted all the medical documents even before She got the request.