Is it possible to communicate with a person electronically between a person(me) with a computer (and no cell phone), and her with a cell phone (and no computer)? Is it possible to send text and links from a computer to a cell phone and visa-versa? I know, I come up with some weird ones but I like to challenge you. She has no intentions of getting a computer because she feels she can do everything on the phone including shop. I am not getting a cell phone right now although I am considering it in the near future.

Yes, it is! I communicate with one of my friends like that all the time. Your friend must set up her phone to receive emails on her phone. I send my friend emails with links and photos from my computer and she receives them on her phone. She responds to the email on her phone and it comes to my email inbox on my computer.