The airways from down south link onto the TMA and descend into the control zone which have more restrictive rules as they are busier airspace.
Not really. The TMA and Edinburgh Control Area/Zone are Class D airspace. The Airways from the South are either Class A (or Class C above FL195) and are therefore more restrictive.
Leuchars has a 5nm radius military air traffic zone around it but outside this zone is open airspace available to all.
The MATZ is also open to civil pilots without restriction, although anyone doing so would IMHO be showing poor airmanship. The airfield also has an Aerodrome Traffic Zone lying within the MATZ, 2.5NM radius centred on the longest runway and extending from the surface to 2000' above aerodrome level. Civil pilots need permission to enter this part of the airspace and, in the case of Leuchars, the notified period of establishment of this zone is H24.