Pending H4 for capped H1B

Hello everyone,
We are going through visa transition from J1-J2 to H1B-H4 cap exempted, my H1B is expected to be completed by April 2022.

My spouse is currently on J2 and pursuing Masters program in USA which is going to end in May 2022. She got an opportunity where her employer is ready to file capped H1B for 2022 cycle. I have following queries.

  1. Can her employer file for Capped H1B while having pending H4 status?

  2. If she gets lucky with the lottery, can she completes her formality of H1B while having pending H4 status.

  3. Is there any option to expedite H4?

  4. What are the different options available for her?