PCSX2 is the only PS2 emulator to consider and they are working on Version 9.9
see both the related links for information on the best working PS2 emulator.
PCSX2 is one of the few that is accepted as actually working
Only if your PC has a working Emulator program can even some PS2 titles be played
No the Xbox could not run an emulator for the PS2
No, a DS emulator is not compatible with the PS2
An Andy can refer to Andy the Android Emulator, an emulator for Android.
There are no working PS3 emulators. The PS2 system has some poorly working emulators that can barely manage to complete some PS2 titles with a lot of work and very poor results on over half the titles. The much more complex PS3 system does not have a working emulator, but it could still be illegal to download Sony Software if it was included in the emulator even if the emulator does not work
Read about the PS2 emulator on the related link
You have to download PS, PS2 emulator and MR roms to play on PC. My Monster Rancher only runs on Android and IOS.
Sorry, but all video game roms are illegal unless you own the game.
There have been some Nintendo DS Emulators developed by some kind souls, however these products are called Homebrews and they require the use of a PSP with Custom Firmware. It can be a difficult process however you can research the information on google and see how you can go about downgrading and moding your PSP so it can play Homebrews. However this is potentially damaging to your PSP and can lead to bricking (aka making it basically useless).