Answer 1:
When you state 'controlled aerodrome', do you mean an aerodrome inside CAS ? If you do, under SERA, you will have obtained an ATC clearance for a VFR transit of CAS. If then you bump into weather, you can ask for an IFR clearance. In practice in the UK, ATC are unlikely to police the clearance they issue on the basis of what you have writted on your FPL. If you take an IFR clearance, you can also transit the ATZ. However, ATC are unable, under SERA, to issue clearances into or out of or through the ATZ (within CAS) unless the METAR for that airfield will permit them to issue an appropriate clearance, i.e. if the METAR doesn't permit VFR ATC are not allowed to issue a VFR clearance. Outside the ATZ (inside CAS) you can self declare VFR (based on your in-flight minima) inside CAS, and ATC have to assume that your are complying.
Answer 2:
If you request a SVFR clearance, and the METAR will support SVFR flight, ATC can give you a SVFR transit of the ATZ. You can only enter the ATZ on a clearance that is compliant with the METAR in that ATZ, so if the weather is bad, you must fly IFR, if it will support SVFR, you can fly IFR or SVFR, and if the METAR supports VFR, you can fly IFR, SVFR, or VFR through the ATZ.
Under SERA, there is a big difference between CAS and the ATZ inside it. You can request whichever clearance you like inside CAS but outside the ATZ, but to enter, leave or transit the ATZ, your clearance options will be based on the METAR within it.
HB