Yeah, unfortunately it's pretty arbitrary and you have to learn as you go... But it seems that for most 'online' or technology communication devices, when we are doing something we say we are "on". For example, "Are you on Facebook?" "Shhhh be quiet I'm on the phone!" "I'm chatting on WhatsApp", etc. If you stored a phone number, though, you would say "I have your number in my cell." But if I did the action and called you, I'd say "I'll call you on your cell."

I think you should practice them come on and test yourself :) http://www.ekolayingilizce.com/wordpress/?p=2114

It could be "I just have your cell number" or "I only have your cell number". If you're wanting to convey that you need another form of communication, such as a chat handle or email address.

I'm trying to think of an answer, but as far as I can tell it's pretty arbitrary. As for your examples, "I'm chatting on/by [app]" is correct, and both 'on' and 'in' can be used in your cellphone example. That sentence should also be "I have your...".