Can I login to facetime on a iMac that I do not use regularly and log off it?

You may have problems using your Apple ID and email address on someone else's Mac...

Using FaceTime

You can, but you have to trust the owner of the computer not to steal your password. It would be easy to do.

I'm saying it would be easy for the administrator of the computer to steal your Apple ID password, if he wanted to. Please don't ask me to provide instructions. I won't.