As I said, ANY training done in the US by a non US citizen requires the TSA security clearance. If you are not a resident of the US, then you will need the correct type of visa to allow training.
Not entirely true.
You need a visa for the training for the issuance of a license or certificate;
Private, Instrument and Multi engine training.
You do not need a visa for; BFR, check-out (on an airplane you have never flown before therefore also training) a tail wheel endorsement, a complex/high performance endorsement.
Therefore also not for night flying. However, you cannot train for a CAA NQ with a US instructor at a school which is not a CAA approved FTO.
You can fly your night time, but no US instructor in his right mind would sign somebody off for solo night. Liability reasons.
Besides, if you want to fly solo night you would need to do the student presolo written exam, presolo flight training of 61.87 and a third class medical.
Pretty useless to go this route, just do your unrestricted stand alone US PPL and get it over with. My 2 cents.....