To properly reinstall the OS, you need to install onto the Macintosh HD volume, not the Macintosh HD - Data volume.
When you install on Macintosh HD - Data, it creates a new data volume and appends - Data, again.
You need to figure out which is your System volume (which would have been Macintosh HD) and which is your Data volume.
I assume your Data volume will be the one with the most - Data suffixes.
The System volume would then be the one with one less - Data suffixes.
You could then Remove all the other volumes and rename the Startup Drive in the Finder. You could use Macintosh HD, or anything you want. If you rename it in Finder, it will rename both the System volume and the Data volume.
For the AppleID, just sign into iCloud using the AppleID you want to use. If you are already signed in with the wrong one, sign out, then back in.
When you sign out, it will ask you if you want to keep a copy of your iCloud data. If you have all of your data associated with the other AppleID, you don't need to copy. If you do, then it will store the data locally. When you sign into the new account, it should upload all of that data to the new iCloud account. You may get duplicates you'll have to manually resolve. You could try deleting the duplicates before signing in, if you can determine which ones are copies.