Quite simply, 'She isn't a movie-going person' means that she rarely goes to the cinema or theatre.
Not to be confused with something like, 'She isn't a dog person' which has connotations of not actually liking dogs.
You can like films/movies but not be a 'movie going person', and yes, you can use the same for other locations.
It is correct as it is.
Anyone caught playing faced fines and even potential jail time.
You could say "anyone who was caught...", but "anyone caught" is arguably better in this context, as it carries more certainty.
Consider warning signs like "thieves will be prosecuted". It wouldn't be quite as effective if it said "thieves who are caught will be ...