Corrected entry: We see the old gentleman travelling this route several times during the course of the film. However he is always going the same direction! Does he teleport the return leg? We know this is a two way line as trains are seen going the other way, including the train father returns on.
Correction: We don't see many things happen, that doesn't mean that they don't. His return journey just isn't relevant to the story.
Corrected entry: It is clear that the tunnel through which the paper chase leads is straight and level. Anyone running from one end to the other will get there quickest by this route. However the three children confidently predict that by climbing up a hill and back down the other side they will get to the other end first, and succeed. This would not happen.
Correction: Several factors would have slowed the boys down while they were running through the tunnel. The boys would either be running over gravel and trying to avoid the sleepers, or stepping from sleeper to sleeper and trying to avoid the gravel. It would be dark, so the boys would slow down, looking out to avoid tripping over things. There is also the fact that the boys had already been running for some distance, and so were beginning to tire and slow down. The three 'railway children' only wanted to get across the hill, so they only had to make a quick 'sprint' in which they could use all their speed and stamina to run a short distance. They were running over open countryside, in sunlight, with full visibility. Plus they did not want to get to the end of the tunnel before the boys, they just wanted to run to a point where they would see them come out of the tunnel.
Correction: The tunnel isn't straight. Pausing the film when the camera is pointing into the tunnel shows the train lines running at a different angle to the position of the other end of the tunnel. The lines would need to curve twice, like an S shape, to align correctly.
Correction: You say that the Railway Children only see "The Old Gentleman"/William Mervyn on a train going one way, but never on a return journey. Although, in both this film, and the original book, we are never wholly certain what he does (or did) for a living, or why he might be travelling on the train, it is implied that he is a person of some wealth and importance, who is respected by important people in London. Maybe he has important business to attend to in London, or elsewhere, that keeps him occupied until late in the day. Therefore he may return home by the last train, which may not come along the railway line until evening, or even at nighttime, by which time the Railway Children would be safe at home, possibly even asleep in bed.