You have the option to work for multiple employers, as long as all employment is connected to your academic degree program.

The cap-gap extension allows for some F-1 students to extend their F-1 status and/or authorized period of post-completion OPT until they transition to the H-1B status on Oct 1. The cap refers to the limit on the number of individuals who can receive H-1B status every fiscal year. The gap is the period between the end of an individual's F-1 status and the beginning of the individual's H-1B status.

You qualify for the cap gap extension until September 30 if the following conditions are met:

Yes, provided you have your travel permit.

The EB-1A (Employment-Based Immigration, First Preference, Extraordinary Ability) is for individuals who have demonstrated extraordinary ability in their field, requiring high levels of recognition and achievement. The National Interest Waiver (NIW) is for individuals whose work is deemed to be in the national interest of the United States, focusing on the impact and significance of their contributions rather than individual acclaim.

Yes, if you start a company.

Yes

An H-1B approval is tied to a specific employer, allowing the H-1B visa holder to work exclusively for the employer who submitted the petition. If there's a decision to switch employers, the new employer must initiate a change of employment H-1B petition on the individual's behalf. While the change of employer petition is pending with USCIS, you may start work for the new employer.

No, there is no requirement that you must have worked for the employer before they can sponsor your H-1B visa. You can be sponsored by a new employer even if you have not yet started working for them.

You can if you have a second concurrent H-1B application. Under H-1B, each employer you work for must file your petition and pay your legal and filing fees to USCIS.