The iPod Touch will eventually run out of battery when it is locked, but it will not drain instantly.
Maybe.
No, you can only turn it off by either letting it run out of battery, or turning it off via the iPod itself.
Let your ipod run out of battery completely then charge it again. It takes a while but its worth it, just leave it alone :)
Only the iPod Touch will run apps. The iPod Nano will not run apps.
Yes, there is a free Flick Home Run app for the iPod touch.
It will vary depending on the capacity of the iPod Touch. The average 8 gigabyte iPod Touch will run at about $199 (excluding tax).
Yes.
If you have enough space left on you iPod Touch and you have updated your firmware to the latest version, then yes, it is possible to download Temple Run or Temple Run 2 on your 3rd generation iPod Touch.
No, you do not need a Mac to have a computer work with your iPod Touch. You can use any PC that has the ability to run iTunes to work with your iPod Touch.
Yes. Yes you can.
iPod Touch FTW ACTUALLY if you want loads of music, and space that will basically never run out, I suggest you get an iPod classic. YOLO
Yes, the jailbreak will be lost. When you upgrade your iPod Touch software, it is completely reinstalling the software used to run it. When you jailbreak an iPod Touch, you are only jailbreaking the software, not the actual iPod.
You probably can somewhere, but you shouldn't NEED to. Unless you have jailbroken your Ipod Touch, viruses and malicous software will not run/work on the iPod Touch platform. Including e-mail attachments.