Hello everyone,
I'm not use if the title is totally correct but here it goes...
I want to connect my Iphone to my desktop or laptop, after that play the games in my Iphone while displaying the game in my actual desktop/laptop.

There are some concerns about it though:
1) Is it even possible?
2) Is there a freeware for it?
2.1) What are the recommended softwares?
2.2) If there are only paid ones, is it possible to torrent it?
3) Is it possible to do it without jailbreaking?
4) Will the games I play on my desktop/laptop be saved back to my Iphone?
5) Is there a limit on which type of games can be played or which type of games cannot be played in this way?
6) Any downfalls on doing this?
7) Is it illegal?
8) Will I get banned on the game if it is a MMO or something like that which has a server?

Thanks in advance~

there are emulators of phones for computers, but iirc theyre buggy as hell and require 4gb RAM minimum

If you jailbreak then you can get Veency which lets you use a VNC client on your desktop to send inputs to your phone. The downfall is that the graphic feed from your device to the computer will lag a lot (but the input from PC to phone should be very swift). You could pair it up with airplaying to your computer if you so wish to, to get smoother video. You won't get banned and everything will stay saved, since it's still running on your phone. Jailbreak detection can generally be bypassed with a flex patch of xCon, but actually installing hacks will likely get you banned. The limitations to playing this way are that on the computer you have a keyboard and mouse, whereas you would otherwise use multitouch.

There's no other way of getting the third party software without jailbreaking.