Video game systems use their own operating systems normally, for example the PS3 has it own operating system that is built in and updated regularly. This said, some systems can use 3rd party operating systems although these are rare and usually pointless. For example Windows 95 can be ported to a PS3 but it pretty pointless and mostly just for show.
Slax is small, portable, and fast Linux operating system. It refers to itself as "your pocket operating system". It is a Slackware-based bootable CD designed with modular approach.
Windows, MacOS, and Linux are the most common.
No. I believe TI83+ and TI84 do use an operating system.
It uses an android operating system.
It uses an android operating system.
virtualization
There are 3: Linux, Microsoft Windows, or Mac OS. Linux has a lot of operating systems under it.
No other system but the PS3
Any gamepad supported by your operating system (such as Windows or Linux) can be used.
No.
You cannot that I know of. For one thing, the ps3 operating system is not an open operating system that allows its user to install random software like windows or linux does. For another thing, running software made for windows (or any x86 system, which is what most game emulators are programmed for) requires an x86 emulator to run on the cell processor of the PS3. So you would need to use an x86 emulator (like qemu) on linux and from there run the gaming emulator. I believe there are some super nintendo emulators that will run on linux on the PS3 without qemu, for example, snes9x. But no, you cannot simply run an emulator from the ps3 without linux. The Ps3 operating system will not run executable files like windows does.