You've really asked two questions here, both of which I think are interesting to answer; I'll attempt to answer them in the opposite order in which you asked t hem. First:
Is this an accepted type of question around here or not?
As others have answered, yes, such questions are acceptable here as long as they are:
- on-topic (which the example you gave clearly would be)
- not plagiarised (it generally suffices to cite the source of any content you did not create yourself)
- not violating the original content creator's copyright (a more complicated subject, which I won't attempt to address here; see the SE Network Content Policy page for more on that)
The short answer is basically that proper attribution makes many such questions acceptable.
The better question is the first one you asked:
Is it a good place to post the puzzles I am solving from this game on Puzzling?
The goal is to give fellow puzzle-lovers the chance to have fun with this type of puzzle.
There are lots of puzzles that are acceptable to post here but aren't at all good. Ideally, a puzzle should have an "A-ha!" moment to it, where you've made some unforeseen breakthrough of insight that makes the solution, or at least the path to it, suddenly clear. A problem with many mass-produced puzzles is that there is no such moment of discovery; they are challenging, perhaps, but much of the challenge is in often tedious elimination of possibilities until only one path remains. Writing a program to generate Sudokus would give you nearly endless original puzzles to post, without worry of copyright or attribution issues no less, but that doesn't mean the puzzles would be fun or interesting to solve.
The goal, as you've said, would be to spotlight a particularly good example of this type of puzzle - one that would ideally be simple enough to show how the puzzles work, but also ignites the interest of the solver by featuring one of those wonderful breakthrough moments.
But keep in mind that well-written puzzles that feature such moments are often not trivial to create, and their creators are more likely to want to reap the benefits of their time investment, rather than have that content given to others without their consent or control by (say) having it posted at P.SE.
Also, because these puzzles are typically created around their "A-ha!" moment, they are by their very nature not mass-producible. That means the total number of puzzles or levels or whatever is probably pretty small; even one of them may well be a significant percentage of the total number available. Sharing even one is thus far less likely to be acceptable "fair use".
Mass produced puzzles tend to be more pastime than genuinely interest-sparking fun, so are the kind of puzzles that maybe can be but probably shouldn't be posted here.
Well designed, interesting puzzles created by someone else would be great to post here, if the author is on board with it. But since these puzzles tend not to be mass-producible, their creators are quite a bit less likely to be ok with having their work distributed outside their consent and control.
My guess is that the Fillomino puzzles in your app fall under the first category here, which means they may tend to be somewhat uninspired, mass-produced puzzles that are probably acceptable but probably not all that good to post here. And, as @n_palum's answer points out, posting multiple such puzzles is likely to quickly lead first to disinterest, then active aversion.
If you find one or two really interesting examples, post (with attributions). I wouldn't post more than that, nor would I suggest posting anything that isn't a particularly noteworthy example.