Domain Mapping, SSL and Cloudflare

I have a WordPress multisite installation running on a domain that is hosted on HostGator. Let’s call it Me.com.

Me.com is set up to use subdomains. It has a dedicated IP, a wildcard SSL certificate and I’m using Cloudflare.

I have a domain (let’s call it Client.com) that is mapped to Client.Me.com. There is a separate SSL certificate installed on Client.com the domain is hosted by GoDaddy.

First, are there specific requirements or best practices when mapping domains and using Cloudflare? So far, the domain mapping is working, but I don’t know know if there is an optimum or SSL-friendly way to map domains when using Cloudflare.

Second, what is the correct way to configure Cloudflare for the subsite? Do I add Client.Me.com as a website in Cloudflare, Client.com, both or neither?

Third, what is the correct way to enable SSL encryption for a subsite that will also be using Cloudflare? At a minimum, I want to force HTTPS for all admin pages and any payment page(s). My preference is that the URL for both admin pages and payment pages show https://Client.com/whaever/ as opposed to https://Client.Me.com/whatever/

I think it looks more professional and raises fewer questions in the minds of the client’s visitors.

Any guidance on getting this resolved quickly would be greatly appreciated.