Unlike ISI, there is no test you need to pass before going to the next highest class, and the group instructors do not administer tests.
At the rink I volunteer with, within the USFSA Basic Skills program, including, I think, Freeskate classes, the group instructors do administer tests at the end of each session of classes - but they only apply to our program, as results are not reported to US Figure Skating.
Likewise, within ISI WeSkate, many (most?) rinks don't report the results to ISI up to some level, because it costs money to do so.
At the lowest Basic Skills and WeSkate levels, I think skating competition organizers, for both organizations, have some freedom about qualifying people for the competition levels as well, since skating levels are usually maintained locally, rather than at the National level.
Given the level of local variation, the local rink figure skating director, or one of the group lesson instructors, might be a better starting point for answering questions about the local rink group lesson program than people, however expert, on an international skating forum, like skatingforums.com.