My back book air goes into a black screen with the mouse curser immediately after powering on and entering my passcode. How do I fix this?

Try booting into Safe Mode to see if you can finish logging into your user account. If this works, then most likely you have an issue with some third party software.

If Safe Mode doesn't help, then do you have another macOS user account on the laptop? If so, then try logging into that user account to see if it makes any difference. If you are able to log into another user account, then there is something wrong with your main user account.