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?

My concern is about the Applying for Citizenship for myself and spouse, and with our passport and GC expiring criteria.
My GC and my spouse’s GC have a expiration date of Sep-2023
My Indian Passport have expiration date of Jul-2024 and my spouse’s on Mar-2026
I am pretty much ready with all the documents (been working on it for some time) to start our citizenship application by myself, according to the U.S Naturalization website for my region (New Jersey) it shows the processing time as 16 months. And if I apply now, during the processing period my GC will expire.
Is it okay to apply for citizenship now and then around July start my renewal of GC? Are there a process to update GC info after a citizenship application is submitted and is in processing? Would any part of GC numbers change when I get renewed? Or would you suggest that I renew the GC first as soon as I can and then apply for citizenship? If I do this then I will have to renew my Indian Passport as well I think, if there is not enough time.