MacOS – Prevent mac from requiring login screen at home

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.

It depends on how the application goes to full screen. If it is "standard" full screen that was introduced with Mavericks, moving the mouse cursor to the top of the screen should reveal the menubar with an option to "restore" the Window size.

Even if it is via another mechanism (vis special code), standard app switcher options should work. your options include:

• Cmd + Tab - swicthes between apps
• F3 on a standard Apple keyboard opens Mission Controls*
• You can set up hot corners (System Preferences -> Desktop and Screensaver -> Hot Corners) to go to desktop or all windows by moving your mouse cursor to a corner of the screen to go to desktop or another app
• Connect an additional monitor (if on a laptop)

*This is not technically F3. It is the shortcut got by pressing F3. You may have to Try Fn + F3 depending on how your heyboard is setup.