re: "My client asked that I use gmail."
That is fine. Many of my clients communicate with me via email.
Email is fine. Skype. Phone. Slack. Facebook. I have met with clients in person.
The requirement is that all payments are done though Upwork. There are no restrictions on how you communicate with clients.
This is not an unusual request, but I strongly recommend you copy into the Upwork messaging system any important message you send to your client via email, phone, etc. And memorialize any important commitments or agreements with the client in the same way.
If you should have to ask Upwork to resolve any disagreements with the client at some point, Upwork will only consider communications between you and the client that are in its system in deciding who said what, etc. No matter how much you like or trust any client, having details in writing in Upwork's files is a good idea.