Core strenght yes. Actually because you are tall this will be more of an issue for you than compact people like me. You can do sonme exercises to suplement, but the best way to accomplish this is climbing overhanging stuff. That generally means relativley juggy. For me this is far more easily done in a great gym.

Top rope. Never been a promoter of top roping longer than you need to, You don't learn the attictude or positions you need to have in muscle memory for clipping or placing gear TR. Far to easy to just go for it and get shut down anyway when on lead.