are installed plugins available to all

Have a look at Multisite Network Administration

There may be some answers under the “Plugins” section in that article.

Yes. All plugins that are installed are available to all users.

If you network activate a plugin, it is installed, and they cannot uninstall it.

Users cannot install plugins.

If you want to control them (i.e. limit who can use what) there are plugin management plugins for that.