MacOS – How to omit directories from Optimized Storage

Is it possible to be tweaked so that OS X won't ask for password when switching users? Or so that OS X won't ask for password in the login screen?

As long as they are not administrative users, yes. (Since you indicated you still want passwords for administrative tasks.)

It is also essential that password is required for any remote login attempts — as they're in the default installation — be it SSH, SMB, VNC or the like.

In that case, you must only allow logins for administrative users.

~/Library/Mobile Documents is basically a mapped network location(to iCloud) and allows you to interact with the documents created by certain apps(default location) most likely they are left over from poor un-installers not cleaning up after themselves or left intact on purpose incase you decide to re-install at some point.

I would contend that it is safe to delete if you don't plan on using those applications, and also assuming if they are generated by an application that when they are needed they will regenerate themselves as needed. Make a copy of them and put them on your desktop and delete them to see what happens. If it breaks copy them back.

On a side note, are you doing this just to keep things clean? Are you in this directory through finder enough that these folders slow your navigation down? I appreciate wanting to keep things clean, however their existence probably won't slow down any indexing by spotlight, use any bandwidth by iCloud or take up a significant amount of HDD space.