We will have a 5:50 connection between flights DEN-FRA(LH) and FRA-FLR (Air Dolomiti) on the same itinerary. We have Priority Pass and we want to
go to Priority Lounge or Primeclass (both in Terminal 2 non-Schengen). We have a couple of questions :

1. United app navigation suggests that we take SkyLine to the T2 (looks like, there is no any security on the way).
But FRA website navigation shows that we need just walk between terminals (I am not sure if we need to go landside in this case).
I read about SkyLine restrictions but it looks like the train for transfer between terminals (non-Shengen) continues to operate as usual
and the United app gives a better option than the FRA website. Is this correct?

Is it even possible to go from T1 to T2 staying in a non-Schengen?

2. What is the best way to go back to our departure gate in Terminal 1, most likely Gates B1-B6.
The United App suggests going through immigration/customs on T2 and taking the train to Concourse B. But, as I understand,
the train on landside does not operate until June, so do we take the shuttle from T2 to T1 instead of train (landside) or we just go back to T1(B) non-Schengen and go
through immigration/customs there. What is the better, more efficient option? How much time do we need to reserve for that transfer?

Thanks.