As I said, I don't use MS Office Live, but it seems that it's a facility that's offered "out-the-box" by MS.
This probably means it's on a server that's configured to its usage - in all likelihood, a Microsoft Server, and that could mean "challenges" if you're not familiar with servers and their settings.
While ZC can be installed on a MS server, it's prudent to install it on a LINUX server, on which appropriate versions of PHP and MySQL have been installed. I recommend looking at one of the certified hosts for this purpose (see hosting link above).
It would mean a unique domain name, but you could think of something like https://www.mydomain-shop.com . or perhaps something altogether different - it's up to you.
Find out where and how your MS Site is hosted, and ask them if they can host ZC as well.
In any event, your ZC site and your MS site would be (functionally) TWO DIFFERENT/INDEPENDENT INSTALLATIONS.