Lost H-1B Cap-Exempt Job, Considering to change my status to B2, and Best Options

[bhagya sree]

My H-1B cap-exempt visa COS was approved on November 20, 2024, but I lost my job on January 17, 2025. I’m considering changing my status to a B2 visa to remain in the U.S. while I look for a new job. My questions are:

1. Can I legally search for jobs while on a B2 visa? If it is legal to search for jobs, should I apply only for non-profit jobs? Or can I apply for profit as well?
2. If I secure a new job, can I change my status from a B2 to an H-1B cap-exempt visa?
3. Is it a good option to go to a B2 visa or is it good to go to F-1 Day 1 CPT universities?