Let's sort out the various sound settings.
Your sound hardware is controlled by the ALSA kernel drivers, the ALSA library provides access to those drivers, and there are various volume/mute controls and you change with
amixer. Some of these settings may also be exposed via Gnome. I usually leave them alone, and only modify things if something doesn't work.
You can save and restore these settings with
alsactl store and
alsactl restore, and the Debian packages
alsa-utils contains a script which restores them from
Pulseaudio runs on top of ALSA. You can change Pulseaudio settings in
pavucontrol and in other ways. Pulseaudio remembers some of its settings, but there's no general way to store or restore them; if you want to make Pulseaudio settings appear on boot, you have to fiddle with the Pulseaudio setup.
As I don't run the Gnome desktop, I don't know what "disable sound alerts" actually does. It may be a Gnome settings, and in that case you have to figure out how to restore Gnome settings on boot. The Gnome settings database has various utilities like
gsettings, but usage has apparently changed over versions and I never could completely understand how everything work.
So, if you are mainly interested in "disable sound alerts", you need to figure out what exactly it does and what it changes.
So the Sound Effect settings are definitely a Gnome thing, so you need to research how to make Gnome settings permanent, or set them on boot.
alsa-utils restores settings on boot by providings scripts for SysV Init (
/etc/init.d/alsa-utils) and systemd (
/lib/systemd/system/alsa-*) which call basically
alsactl restore /var/lib/alsa/asound.stat). So when you call
alsactl store as root, it will write the current settings to this file, and they will be restored on boot.
It's possible that the "selected" output shown in the Gnome menu is a wrapper for the default Pulseaudio sink. You can set this sink with
pacmd set-default-sink (use
pacmd list-sist-sinks | grep name: to list the name of the sinks), and I think in
pavucontrol, too. Pulseaudio will remember it. It's also possible that this is again a Gnome setting that overrides what Pulseaudio does.