1: I had the same thing happen to me, once. I can't say that feels very realistic but then, I never flew one in real life.
2: The roll is mostly induced by the propeller spinning, the plane tries to spin with it. Its possible that changing the elevator trim messes with the plane's aerodynamics and messes with the roll trim. Just keep trimming.
P.S. I never read the manual or did the training missions so i might be wrong. All i said was based on games other then DCS.