Hello, I'm new here and have a question for you

I'm thinking of booking a trip GOT-FRA-AUH-MEL, with LH on the first leg and then EY, on the way back its same routing just SK on the last leg.

Connection times are 1h 25 min and 1h 50 min on the way back, will this be enough as Frankfurt is a big airport, will the luggage be checked in all way if I buy the trip on one ticket? And how about boarding passes?

If i'm so unlucky that I miss a flight becuase of delay, weather or something, who should I turn to, LH or EY?

Wow, that was many questions, hope you can answer them!