The ANO in the UK automatically validates an FAA licence for use on British aircraft. It may not be so simple in all countries. The question is whether a flight school would accept that. In my experience schools are very sceptical about FAA licences and even JAA ones, normally requiring a 're-training' period, sometimes upto 5 hours, in order to adapt to the different conditions found in the UK.
If flying at night under SVFR you are absolved from the IFR requirements and therefore this is permissable.
I would find a source for RSFTO's suggestion that any radio licence will do. I would have imagined that your radio licence must match your pilots licence. The ANO would be a good start.
To get your FAA radio licence, start here and register:
FCC Universal Licensing System (ULS): ULS Home
You are wanting a 'Restricted Radiotelephone (non-limited)' licence. The process is not particularly clear, but they are prompt with the paperwork.