Assign root user password after installation
The problem is with incompatible data files created by a different version installed in the past. The errors show the old datadir was left from an old installation that is not compatible with 5.7.

If your database does not contain any useful data yet, simplest way to fix it is to clear the datadir and let the new version initialize it fresh.

Uninstall 5.7, purge the datadir, and then reinstall. Normal uninstall won't clean it, gimp does not delete your images on uninstall either. You need to delete and reinitialize the datadir, not the application packages. It might be at /var/lib/mysql/ (the default).

If you already have some data in the database you want to keep, you should instead follow the instructions for upgrades.