No passport control either way as long as you use the Skyline train but you will almost certainly have to clear security in each direction.

Your flight from EWR is likely to arrive at a Z gate or possibly a bus gate at the bottom of A/Z pier. Although you can probably enter Z pier behind security, in order to enter B departures where your flight to ABZ will depart, you will have to clear transfer security due to the layout of FRA T1. The only way to avoid security is to go through passport control twice (to enter and leave Schengen) but this is not recommended unless you can use ePassport gates.

Although the UK is a 'clean' country most flights from the UK arrive at a B gate and there is no way to connect from non-Schengen B to any flight without clearing security. Very occasionally ex-UK flights arrive at a Z gate which means you can walk to your departure gate in Z without passport control or security but it's unlikely to happen in your case. EDI flights are likely to arrive at a bus gate at the bottom of A/Z (different one from EWR arrival) and you will have to go through transfer security at the top of the escalators before going down to Z departures.