"But if I did IDk what he would say that would make me feel better."
"but I just wish he would come hang out with me, even play a computer game over the Internet, or pick me up & take me to the hosp. ANYTHING."

Sounds like maybe you just want to connect with him, and he told that its fine to e-mail or call, so I think it'd be okay for you to do that -- maybe you don't need him to have great wise words so much as just a sense of his presence/connection. I've noticed a lot of people on the boards express a need like this sometimes and they and their therapists seem to work with it. The biggest thing is that your therapist said it is okay to reach out if you need it.

That's very different though from being truly in a crisis, in which case it is probably still appropriate to call T but keep in mind he's going to reach out and try to find people who can address that issue (i.e. calling 9-1-1).

This sounds like something it'd be really important to be clear about.. I hope you can talk to your therapist about this when you meet with him sometime! I would hate not knowing!