Is H1 still valid if I quit my job and go back to India

I am currently on H1 visa. If I quit my current job and go back to India, can I still apply for jobs in USA from India? Will my H1 still be valid or will I have no visa?

If so, will I only need H1 transfer or will my employer need to apply again for me ?

Your H1 will be active until the validity period. You can apply for jobs in US and can come back to work in US provided your H1 is still valid. Once it expires you have to go through renewal process at the consulate