Bucks operates an equal preference system, so that there is no tactical advantage to be gained by "gaming" the choices. Put simply, a parent's first choice is exactly that and if a place can be offered it is. If a place can't be offered there, it effectively disappears from the list and the second choice becomes the new first choice. The schools do not know where on the form an individual parent placed them so no-one at the school or the council sits there thinking "they only put that as second choice so we'll move them down the list".
In the scenario you outlined, school A was first choice and was able to accommodate the child, so that's it. Had school A been put in second position and school B was unable to offer a place, the child would still have been offered school A because it would become the first choice. I'm not up-to-date with Bucks transport policy but I believe that they will only contribute to travel costs for the closest school and only if it's beyond a certain distance away from home. By choosing school A, the parent has willingly applied to a school further away and so travel isn't subsidised. If they chose school B in first place and a place was allocated, travel costs might have been funded if they met the distance criterion.
As to your last question:
Quote:
...when allocating places, is a catchment applicant who puts a school for which they are qualified as their second choice ranked more highly than a non-catchment applicant who puts it as their first choice?
I think the answer is yes or no! If the catchment applicant wasn't able to be placed at their first choice school, the second-placed school then becomes their first choice and yes, they would be ranked more highly than the non-catchment applicant (I'm assuming the non-catchment pupil lives further away than the catchment applicant). If they were able to be placed at their first choice school then no, because they wouldn't be ranked for the other school.