Why are some players locked from being cut and are described as "Will have already started playing at claim time"?

By default, Fleaflicker prevents players from being cut after they lock according to your league's lineup locking rules. If you want to cut bench players even after their games start, you can enable that from League » Settings » Edit Transaction Rules » Prevent Cuts After Game Start » No.

Note If you do this, starters are eligible to be cut the morning after their game starts and bench players can be cut any time. The reason we don't enable this by default is because in weekly lineup leagues, selecting no for this option allows owners to exceed the roster limit for a given week by dropping a player who locked early in the week and adding a player that has not yet locked for the week. Selecting no also allows owners to unfairly manipulate their bench score so the "Most Bench Points" tiebreaker will not be used.