Is banking regulations act is applicable to all private &

Dear Professional Friends

Come to know RBL bank is giving good interest on FDs.

My doubt are as below, please clarify

1. RBL (https://www.rblbank.com/index.aspx) is a private or public sector?
2. Keeping Fixed Deposits in this bank is advisable or not?
3. Is Banking Regulations act is applicable to all PRIVATE & PUBLIC banks in India?

Advance Thanks

Cheers

Balaji Subbu