F-1 Visa

I am on an F1 visa, and My spouse is on a Green Card. My Green Card through my spouse is under processing(I-130 under Review). I am graduating in March 2024. My questions are as follows:

At what stage in my Green Card Processing can I start traveling outside the USA?

Let us consider my GC is still under processing by the time I graduate and enter the job market:

A)Can my employer file an H1 while my Green Card is under processing?

B)Given my H1 got picked, will there be any issue for me to travel to India to get my H1 stamped?

I am in the F1 OPT period and I worked with Amazon from August 2022 to May 2023. My H1B got picked in the lottery this year, and got it approved in June 2023. Currently, I’m in my 90-day period of unemployment, and would possibly get a new job with another employer before it ends.

I don’t want to lose my H1B this year. Is there any way that I can transfer my approved H1B to the new employer?

Currently, I am holding a STEM OPT from May 2022 until May 2024 (2 years).

My employer had applied for H1B this year and last year but had no luck.

Question and suggestion, please:

1) What are my legal options?

1.1 Apply for H1b next year in March and wait for the result, In case H1b is picked, how do I process it as my STEM opt expires in May 2024?

2) Enroll in university for the Master's degree?

2.1 I have a few classes remaining for my master's as I have finished my bachelor's degree in the USA and I take Day One CPT? Once a master's degree is complete, reapply for OPT and STEM OPT.

2.2 Should I continue to apply for H1B in the meantime?

3) If I apply for Master and Day One CPT, do I need to enroll for May–August 2024 (the summer class) or can I enroll for Fall 2024?

Note: STEM OPT Expires: May 15, 2024, or please suggest any other better option to stay in the USA.

Lastly, my passport expires in May 2024 as well. Is there any problem there?

- I'm thinking of starting the process for the renewal online. Should I do it now or wait for some time?