mtb discs on a cx?

As long as the pads are suitable and the disc is the correct size and fitment, no

Depends. There are actually two versions of the BB7s; if you want to use them with road levers, you want the road version, which is set up for the right cable pull.

When it comes to hydraulics, there's probably not much point trying to use MTB kit (other than the disks, obviously). If you're getting hydraulic road levers they'll presumably come with calipers anyway; same applies to the hybrid systems (Parabox, V-Twin). You could theoretically use MTB calipers if you match the piston sizes and brake fluid type, but unless you're trying to solve a very specific problem there's probably little point.

Monty Dog wrote:

I built my first drop-bar disc bike over 12 years ago, way before they were available on the mass market so had to make do with what was available. I did play around with some MTB cable disc brakes - OK on the rear but did fit a BB7 road on the front to give more modulation.

I did the same, as there was no such thing as BB7 road at the time. I did find the BB7 MTB to be extremely good, but the pads have to sit extra close to the rotor if you use road levers, which means lots of rubbing.