Regarding how and where to install the web client and GP, I would refer to the manual provided by Microsoft for installation and setup (link is below, you will need a CustomerSource or PartnerSource login).
As long as the custom web domain points to the public IP address of the IIS server where the web client is installed, they will be able to use that. You'll have to check with the domain registrar as to how to point the domain there as every registrar is slightly different. It will need an "A record" pointing to the public IP.
mbs.microsoft.com/.../MDGP2015_WebClientServicePacksHotfixes