Hi envirossf,
Reinstalling the Avast Mobile Security (the antivirus app) or Avast Cleanup will not affect Passwords on your phone, so you can reinstall those apps as/when you would like.
From what you have described happening, it sounds like the only workable solution we have is to delete the synchronization group for you so that you can start again.
This will wipe any saved passwords that you currently have in the synchronization group, but not those stored on your current devices
if they are not currently synced. This means that if you have any logins saved on your phone, those logins won't be deleted as the phone is not currently synced. Due to the issues you were seeing when you were trying to sync the PC, I would also recommend that you reset the password vault currently saved on the PC before trying to sync it, which means that you would lose the passwords saved on your PC (which you have already printed out).
So, the process I would ask you to follow is:
1. Confirm if it is okay for us to delete the synchronization group, and wait for me to confirm that it has been done.
2. Reset the vault on your PC - to do this, please follow the instructions in this support article:
https://support.avast.com/article/163/3. Set up Passwords again on the PC according to the steps in the first section of this support article:
https://support.avast.com/article/259/4. Sync Passwords on your PC according to the instructions to "Synchronize your first device" in this support article:
https://support.avast.com/article/255/5. Sync Passwords on your phone according to the instructions to "Synchronize subsequent devices" in the same support article:
https://support.avast.com/en-us/article/255/#idt_0206. Re-enter the passwords that you have printed out, and check that they are copied to the other device.
Under this method, you do not need to remember the passwords used several years ago for either the Avast account or the Master Passwords. However, please make sure that you log into the Avast account in the same way on both devices (i.e. if you log in using email on the PC, please also log in with email on the phone - if you use Google to log in on the PC, please use Google to log in on the phone as well).
Please confirm if you would like us to delete the sync group for you.