@KaneLives - If you are getting a never ending rotation of bistro chefs who never stay on duty, yes those will get dumped into the unassigned homeless population and the game might quickly run out of helpful things for them to do. Strongly suggest Ani's Business As Unusual Bistro mod if you aren't already using it, the chef and waiter assignments are stable once it's all set up, they can work different shifts to keep the place staffed throughout the day, etc. And the chefs and waiters do not have to be homeless if you assign those slots to residents.
<a href="http://nraas.wikispaces.com/Business+As ... +Bistro</a>

Other than that, I can't answer why the your number of homeless sims keeps rising because I cannot see into your game and there could be many reasons. When I get this kind of thing, I'm usually able to figure out who the new not so much wanted arrivals are by way of MC Status reports on them -- are they actually Role Sims, Showtime street performers, homeless co-workers and bosses (commuters) being assigned for the residents in town if there aren't enough other residents to take up those slots. It does sound like something is a bit out of balance here, though the chefs could be a heavy factor if they are spawning multiple times throughout the day. The game doesn't just generate homeless sims for no reason at all, but figuring out why it's doing this (could be multiple factors) can get challenging.

I'll have to defer to others here on the Simfest questions, I don't have the patience to make those things work right and tend to remove or lock up the lot when Showtime related things continuously malfunction.

@luftspeiler - Those are more like clues than well-defined categories. Homeless Vagrant means the sim is homeless -- has no residence of their own in town. This would include homeless Role Sims not currently working at an assigned station such as festival workers in between seasons and homeless co-workers and bosses that get spawned when there aren't enough residents to take up those slots -- we think of those as commuters, coming "into town" each day to work or perform and then they go off the map or into darkened out rooms with private room markers in LN style apartments to hibernate when they aren't needed. They aren't typically stable in the sense that they may leave your game and possibly be replaced by others over time.

Out of Towner is a sim whose homeworld is elsewhere. Could be tourist mini-sims or sims whose homeworld status is not able to be determined. Chain or one of the others may be able to offer more precise definitions than those.

Afraid I don't have much experience with the Sim Finder or the Wishing Well, but I expect the sims generated from those get added to the homeless "household" and may or may not be used to fill Role, co-worker, and street performer slots as called upon. Or they may just wander around town for a while and get used as "extras" to populate community lots.