For host-level backup, because Xen always uses Linux as its privileged domain, and because Unitrends supports a flexible file-based Linux backup paradigm, you can use pre- and post-commands to save and restore the VMs at the host level.
No guarantee of Linux with Xen. It is very common but Xen is unique in that the Dom0 is "pluggable" and many different OSes can be used. There are a few BSD family members and Solaris that are good enterprise options there. Linux is clearly the leader in the Xen space, though, with adoption I can only guess in the 99.999% range.
Honestly If i'm a BSD shop and paranoid (looks at our web server) you use jails, or if your Solaris you use zones. Most mixed shops are going to stick with Linux.
Well you use it because it is your virtualization platform, not because you are paranoid. Linux is definitely the vast majority.
Referring to my half joking reason for why my companies front facing webserver is hosted on FreeBSD. BSD is notorious for being used by the most paranoid of admins. I believe it is hosted within a jail which is then hosted on vSphere 5. The reason for BSD over Linux reason is our VP of operations is long time BSD user and he outranks the RHCE on staff. Honestly I can't complain about executives who choose platforms based on geeky OS bias's its no worse than the ones who don't know what BSD is. Looking back at Netcraft's what is that site running I need to give him hell about why for one day we were hosted on Windows 2000.