For all I know, you must 'Jailbreak' it. I think there is a way to screen record using a capture card, but I am not sure!
No there is no app that allows you to record your ipod while playing games without jailbreaking it first.
no
It is impossible to get an installer on an iPod Touch without jailbreaking.
You cannot get all apps for free without jailbreaking an iPod Touch. It is not possible.
no
No
No, not without jailbreaking your iPod 2g.
You can't.
You can't.
you can't.
you can, but it requires you to jailbreak your ipod. this is not recommended if you have a warrenty, because jailbreaking your ipod would be voiding your warrenty.
Yes; not jailbreaking it. If you mean a way to do the same thing as jailbreaking without actually doing so, there is no current way to do so.