Can towns be founded during a game in OpenTTD

They'll go anywhere. Passengers in OpenTTD are treated just like any other types of goods - sent them to the next block, or 3000 miles away (preferably through something faster than a bus) and they'd happily pay you for the trip. Supply and acceptance of passengers are separate, and do not affect each other.

The problem you're having is probably because the stations are overlapping each other too much - meaning they are competing with each other for passenger. You're also building some of them out of the town, which means that though they accept and supply passenger, in reality, the amount is minuscule.

What you would really want to do at this stage of the game is to build one or two station in the center of that town, then transport the passenges picked up there to another town (preferably of similar population, or two smaller towns), so that you are covering enough distance to get a good sum of money out of each trip.

I went digging in the source code (gotta love open source games...)

First, you have to pass a random check for success (I haven't been able thus far to trace back what the "default" value for this is...), and then the game will attempt to place the new industry in a random location. If this fails, it tries to orient the industry differently, until it runs out of potential orientations. It then picks another location and tries again, up to 5,000 times.

Height doesn't appear to be a factor, but proximity to another industry of the same type does, and I believe that it's checking to make sure it can "land" the industry on flat ground.

The lesson here is twofold - one, there's a chance to fail, period. You might just be unlucky. Secondly, there's a chance that it will attempt to place a new industry and fail, due to bad luck or overcrowding when picking the tiles to place the industry on.