General Nonimmigrant Visa

I am on an H-1B visa and recently got laid off.

If I don't find a job within the 60 days grace period:

1. Can I go back to my home country and keep applying for jobs and then come back once I get one? If yes, would I have to go through the lottery again?

2. If not, what are my options?

3. What additional documents do I need to provide while applying for my new visa to explain the missing pay stubs?

4. What does the company that let me go send to the USCIS as documentation for termination of contract?

I got a H-1B approval in 2020 and stamping was done in 2022, due to personal reasons, I have decided not to travel to the US. My question here is at a later point in my career, will I be eligible for the CAP exemption for the different sponsor, even If I never visited the US using the stamping? Also whether this cap is exempt till 6 years from approval time or forever(but the 6 years clock starts from the time I enter the US)?

I am currently pursuing 6-month online certification program in "management" domain from the Indian Institute of Management (IIM) here in India and this IIM has been awarded the EFMD Quality Improvement System (EQUIS) accreditation by EFMD, the globally recognized international organization for management development. This institute has AACSB (The Association to Advanced Collegiate Schools of Business) accreditation in the US. I have bachelors in chemical engg from India and masters in chemical engineering from the US. I plan to use the H1B remainder option to come back to the US and would like to change careers.

My question is as follows :
1. Is the "online certification in management" that I am currently pursuing from the AACSB accredited institute as mentioned above considered valid and acceptable by the USCIS for changing careers from chemical engineering to managerial roles such as e-commerce/software domain on H1B?
2. I have also done courses in management, data analysis, economics, computer programming and other math related courses at undergraduate level in chemical engineering and would like to know if these courses would be of any help to change domains as transcripts for bachelors and masters degree are requested during the H1B processing?

Question 1: If H-1B transfer is approved but not joining the new employer, then what all is required to be done to avoid any problems? - Is it required to withdraw all approved H-1B transfer petitions in that case?  What is the validity of H-1B transfer approval?

Question 2: I am currently working for Company “A” on an L1A visa which is valid until 09/12/2024. I have my i140 approved that was filed by company “A” in EB2 with May 2019 as the Priority date. I am from India. Company “B” filed my new H1B.
My new H1B petition (I 797A, notice of action) and accompanying request for a change of status got approved on Dec 21st 2022. Employer “B” shared with me the approval copy only on 29th Dec 2022. I 797A, notice of action says my new I 94 is valid from 12/21/2022 until 10/10/2025. Will my work authorization status in the US reflects as H1B only if I submit my new Form I-9 through employer B? or is it already effective from the date of H1B approval i.e., 12/21/2022?
Is there a time limit within which I have to resign from my current employer “A”? What’s the maximum number of calendar days I can continue with my current employer “A” from the date of my new H1B approval i.e., 12/21/2022?

1. I am on H1B VISA and was notified that my employment will end on January 20th. I am actively seeking new job opportunities. Can you please let me know what happens if I am still interviewing after 60 days and become out of status? 
2. Do I have any other options to change my VISA status before/after my employment is terminated and I fail to secure a job before the 60-day period is over? 
3. Does my VISA become invalid after the 60 days or can I still find a job and reactivate it if I get an offer after the 60-days?

Have any rules changed regarding getting a spouse visa through H1, L1, or O1? Also is traveling on a tourist visa to the US after marriage not ok, with a pending GC application? Finally, does the US have any special agreements with the UK, EU, Singapore, Dubai or Australia for visas that may qualify in this scenario?