In june I am going US with my husband on H4 Visa, can I work for Indian company?

My company is agree for remote work, but is it legal?(My company not registered in US)

Or if I resign, can I work as a freelancer for Indian company?

What I can do to work for Indian company remotely.

How can I convert my H4 visa to working visa, can I apply myself for working visa?

When on H-4, you CANNOT work period. It doesn’t matter whether the work is online, offline or a company not registered in US. You just cannot work.

In order to work, you need a company to file H-1 for you. Once approved, you can work on H-1. Or get H-4 EAD for which your spouse needs to have an approved I-140 or be in 7th year of H-1.

Can I study? how can I apply, is their any certain criteria, I have done MCA.

You can study on H4 but are not eligible for CPT or OPT. You have the option to move to F-1 visa and become full time student and avail CPT, OPT etc

can I myself apply for the H1 visa? If yes, then how?

Only an employer can apply H-1 for you. You need to find an employer, and if they plan to hire you, then they can file H-1 for you. There is no self-filing.

i cant work by free-lancing also? no work, means no work!!

Like you said “no work, means no work!!”. Is your spouse close to getting his/her I-140 filed or entering 7th year on H-1? If yes, then H-4 EAD is an option which would then allow you to work.