No – you might be able to squeeze in skinny cx tyres but the clearance on the brakes and the rest of the frame will be crap. Touring bikes (which often have canti brakes can often be converted though)
Also, the geometry is different – typically shorter on a cx bike.
Possibly. But many road bikes have very little tyre clearance available. CX bikes use canti brakes rather than dual-pivots partly to get sufficient room.
Road bikes used to be built with the room available. My old Freddie Grubb has big top-pull brakes and runs 32mm tyres with fenders. It could easily run a 35mm CX tyre with mud room. Modern racers aren’t done like that. If you’ve got something more tourer/commuter then it’ll work better.
This thing was built in the 1970s as a standard enthusiast’s bike, for racing, training, clubruns, weekends, CX and whatnot.