Can my Apple ID be suspended or banned for jail breaking?

I want to jailbreak my iPod touch and I also have an iPhone that will remain unjailbroken and I want to use the iPod touch for iMessage and other things so can I get in trouble for using jailbreak?

No.

I suppose they could in theory, but I don't believe they've ever done that. When I used to use iDevices years ago, I would always jailbreak them (if possible) and never had any issues with my Apple ID.

In short, don't worry about.

I guess they can be, yes