find / -lname '/path/you/are/looking/for/*'

Note that the -lname option is a GNU find extension and may not work with other find implementations.

Nope. Free beer ≠ free speech.

That was many years ago, so I don’t remember all of them. E.g. Chromium was unable to display pages (was it installed from testing? or it was from stable but some of its dependencies from testing? I forgot).

Yes, this is possible if you configure preferences (see man apt_preferences). However if you install numerous packages from testing, this can lead to various bugs. I used to do such installation and concluded that it is better to avoid this.

#!/bin/sh
printf 'ABC %s: ' "$(date --rfc-3339=date)" | xclip

User settings are stored in the home directory, so you already have them backed up with rsync. If you didn’t omit dotfiles, of course.

What kind of changes? Package installation, removal and configuration? Use apt-mark showmanual to save list of manually installed packages, dpkg --get-selections | grep 'deinstall$' to save list of removed packages, debconf --get-selections to save debconf package settings, backup files that you edited in /etc. This should be enough for restoration, wouldn’t take a long time for backup and avoid risk of filesystem inconsistency.

The standard answer: don’t backup the system, automate its deployment instead. Backup only data.