Hey again! Sorry those suggestions didn’t work out. Did you have an external hard drive you can use to save your data? If so, I’d format the External drive in Disk Utility (as Mac OS Extended Journaled and GUID scheme), Quit Disk Utility then Reinstall Mac OS but choose the external drive as the destination instead of Macintosh HD. Then when it’s finished, it’ll boot up from the external drive where you can either:
select the option to move data from Macintosh to external drive.
OR:
Set up like new, create a new user, the use Finder to select Macintosh HD (Under “Locations”, then open “Users” folder and move your user folder somewhere onto the external hard drive, (Such as downloads). (I’d refrain from signing into your Apple ID during set up, or just make sure you don’t move the original user folder into iCloud Drive (Desktop and Documents), if enabled, as it may use up your iCloud storage, which is why I suggested Downloads.
Once that has transferred, you can shut it down, eject the external drive, boot to recovery mode again with Command R, THEN reformat, (Erase), the main hard drive (Usually Macintosh HD), (Just make sure you select “View > Show all devices” from the top menu, then erase the main hard drive (On top of Macintosh HD, usually AppleSSD or AppleHDD), if installing Catalina again make sure to choose the format APFS and again GUID, then erase).
Once done, you can then reinstall Mac OS onto the main hard drive (Macintosh HD), then set it up as new, (Or select the option to transfer from the external hard drive......I think best to set up as new to avoid further issues), then you can use the Finder to drag and drop data from the external hard drive to your newly re formatted Mac!
Its a lot of work, but if the data is important it’s definitely worth it.
It May also be a good idea to run a hardware test by starting up you Mac holding “D” on the keyboard. Whatever it finds wrong, it’s best to follow these steps to save your data if possible.
Once done, you can reformat the external drive, and set up Time Machine with it to avoid future data loss:
https://support.apple.com/en-us/HT201250
Hope all goes good, cheers!