Yep, on either engine test runs, or charter "go supersonic" flights.
Nope, specially planned and briefed flights.
Concorde flew a figure of eight route, NW up towards Scotland with a right hand turn followed by a SW leg back towards the Wash. Speed was M2.0 at FL560 with slight height variations to maintain constant speed.
Fighters had several prearranged CAP points and were only briefed for frontal fox 1 shots, the stern intercept IIRC was not briefed and resulted in an interview.