Don't worry too much about the change from International terminal to domestic (or vice versa on the return) in Istanbul. I've done that route several times & there was always a member of Pegasus groundstaff to guide us through. Just be aware that if the timings are particularly tight, you're kind of expected to run with them! After the first time, I got hand luggage with wheels, which made life a lot easier.
Also, if you buy duty free in Stansted (or on the plane on your outward journey) make sure it is sealed in the bag, & explain that Istanbul is not your final destination, otherwise it may be confiscated at domestic security.