You can chat on Gmail using the Hangouts. It is the official Instant Messaging app of Gmail. You can start chatting on that using iPod touch too.
yes
You can sign out of the Gmail from your iPod Touch. You need to go to Accounts where accounts of all apps are there. You can sign out from the Google ID there.
No
With the free Skype app installed the iPod touch can do video chat on Skype. (See links below)
Yes, you are able to access Gmail (and most any other email) from your iPod. If you don't want to get the gmail app, just click on the mail icon on the bottom of the screen. Then you just enter in your email and password, and you can receive and send emails from your iPod Touch.
You can use FaceTime on a Mac to chat with an iPod Touch (See links below).
You Cannot Chat in Ipod Touch or Iphone only in a Ipad
you cant stupid
The ipod touch 4g can video chat with an iphone 4 if you have a WiFi connection.
Gmail mobile is an application for a mobile phone or ipod touch where you can check your email from Gmail with either wifi or 3G internet services.
No, not like video chat on your email. But of you have the iPod Touch 4th generation you can use FaceTime, which is pretty much video chatting but the other person must have an iPhone 4, the 4th gen iPod touch, or a newer Mac with the FaceTime application.