Encrypting salted password hash before storing in the database

I have read here, that instead of using pepper, it is better to encrypt hashed/salted passwords before storing in the database. Especially with Java, as there’s no library for salt/pepper, but just for salt hashing, and I’m not going to implement my own crypto in any way. Have questions about it:

  1. Is it true? Will it add security, if db server is on the another physical computer, and encryption keys are sored on the app server’s fs?
  2. If so, is it ok to use RSA for hash encryption?
  3. To check password in this case, is it better to read encrypted password from the DB, decrypt it, and then compare it to the hashed/salted one entered by user, or encrypt entered hashed/salted password and then compare with the encrypted value in the database? In this case, will it be the same as using another hash, as encrypted hash is never decrypted?

Thank you