ithemes security should be left alone. It is a security plugin and should run on every page.
Audit log plugin should be ok to disable on the front end and only run in the admin.
Plugin Organizer you can disable but it keeps itself active where it needs to be active and disables itself where it needs to be disabled by default. That prevents you from locking yourself out of the options.
My theme updater plugin should be ok to disable on the front end and only run in the admin since it sounds like it just does updates to your theme?
anti-SPAM plugin should be left alone unless you can figure out where all your comments are submitted to and only enable it on that url. If it needs to load things in the comment form then you’ll need to have it enabled wherever you have comments enabled.
Yoast does something on every page. So that is really up to you where to disable and enable it. If you know where you wont need it you can disable it there.
W3 Total cache should be enabled on every page since it does something on every page.
Autoptimize does something on every page so it should be left alone.
I’m not sure what disable emojis does exactly so that is up to you if you want to disable it.
Plugin Organizer can change the scripts and css loaded on a page. So it can cause problems with both Autoptimize and W3 Total Cache. They rely on the same plugins being loaded on every page. So if you have a plugin that loads a bunch of javascript and css and you disable it for a page but not for another the caching plugins will recache the page all the time because the content is changing. W3 Total Cache can also prevent a plugin from totally being disabled because it will cache the page and then serve the CSS or scripts from plugins that are not active. Or not serve them from plugins that are active.
In the end it is on you to understand what you are doing and how your plugins work. I can’t really tell you how your site will act with different plugins disabled. The best thing to do is to do testing with different plugins loaded and see how your site performs.
