Most toilet problems trace back to one of a small set of parts inside the tank: a worn flapper that will not seal, a fill valve that runs too long, or a flush valve seat that no longer closes fully. A running toilet almost always means one of those three, not a problem with the bowl itself.
A toilet that rocks at the base, or leaks at the floor when flushed, usually points to a failed wax ring or a cracked flange rather than a tank component, and that is a different repair entirely, one that involves lifting the bowl rather than opening the tank lid.
Either kind of repair gets tested with a full flush cycle and a check at the base before the visit is considered finished, not just a quick look inside the tank.