I have the minimum, mean, and maximum of some data set, say, 10, 20, and 25. Is there a way to:
create a distribution from these data, and
There are an infinite number of possible distributions that would be consistent with those sample quantities.
know what percentage of the population likely lies above or below the mean
In the absence of some likely unjustified assumptions, not in general - at least not with much sense that it will be meaningful. The results will depend largely on your assumptions (there's not much information in the values themselves, though some particular arrangements do impart some useful information - see below).
It's not hard to come up with situations where the answers on the proportion question may be very different. When there are very different possible answers consistent with the information how would you know which situation you're in?
More details may give helpful clues but as it stands (without even a sample size, though it's presumably at least 2, or 3 if the mean isn't halfway between the endpoints*) you won't necessarily get much of value on that question. You can try to get bounds, but in many cases they won't narrow things down a lot.
* actually if the mean is close to one endpoint you can get some lower bound on sample size. For example if instead of 10,20,25 for your min/mean/max you had 10 24 25 then $n$ would have to be at least 15, and it would also suggest that most of the population was above 24; that's something. But if it were say 10,18,25 it's much harder to get a useful idea of what the sample size might be, let alone the proportion below the mean.