I hold H1 Visa, can I apply for F2

I hold H1-B Visa. Can I apply for F2 also.

Will my H1-B continue to be valid or will it be cancelled.

And in case I travel on F2 can my status be changed to H1 if I find an employer.

Thanks in advance!

Yes, you can apply for F-2 visa. When appearing for F-2 visa interview, there is a possibility that officer will cancel your H-1 visa stamp w/o prejudice when approving the F-2 visa.

Even then you can move to H-1 in future using the old petition as reference.