That password protected wallet file remains password protected, even if you import that into a new electrum wallet ?
No, the password you set up only encrypts the wallet locally, if you or an attacker imports this wallet with the seed phrase on a different device, you'll have access to spend the funds on the wallet and set up a different password for the wallet on that device.
Also if i make a wallet without password protected wallet file, can i convert that later to password protected ?
Yes you should be able to do that.