For BASE jumping, many start with sky diving or jumping from relatively easy exits like bridges.
Most free solo climbers climb with a rope for the majority of their climbs, although exceptions like Paul Preuss exist. They often rehearse free solo projects many times on rope before going free solo, although there a notable cases of 'onsight' free solos like Hansjörg Auer's 'Weg durch den Fisch'. In the case discussed here, Alex Honnold apparently climbed Freerider around a dozen times on rope and rehearsed the crux pitch many more times. He did take several falls on the route, one of them spraining his ankle last summer.