All of your questions are good ones. Because of the long time interval, unfortunately most of these "clues" or reported sightings have become legends associated with the story. Like second hand or third hand information repeated so often that they become intermixed with the actual facts of the case.
Looking at the map and reading the story, my gut feeling is that Jackie started out in the wrong direction, moving west instead of north. After walking for four to six blocks in the wrong direction, and seeing nothing familiar, he came to the highway - which he probably had been told not to cross. And at this point; hungry, confused, and frightened - one of two possible scenarios occurred.
First, someone in a passing car may have indeed picked him up - more likely between 1 and 2PM. Had the car been traveling generally NORTH on Hwy 23 (the side Jackie was probably on), then that car would have proceeded down "main street" and past Jackie's house on the way through town. This would have been a big risk by a would be kidnapper.
Secondly, Jackie might have realized his navigational error when reaching the Highway, and then turned north toward the Creamery. Certainly he would have known his way home from there. But perhaps he was seen by someone there and taken toward the river, and then to a train car? Knowing what the train schedule was for September 1944 might provide valuable clues. Jackie could have been thrown from the train somewhere between Paynesville and the next stop on the line, or might have been taken to a camp of migrant workers.
The problem here is with the sequence of clues. Most likely the reports of sightings of Jackie by the Highway at 1PM and 4:45PM came first, and police focussed on them in tracking down the men in the gray car.
As is so often the case, the scenting dogs were not called in until a few days later, and AFTER rainy, cold weather had set in. The dogs did not track Jackie all the way from the school, as implied by the story, but rather PICKED UP his scent by the Creamery and tracked him moving West toward the River rhere the scent ended (but note that the railroad was also right there).
Scenting/Tracking dogs are absolutely unbelievable in their abilities. A well trained dog knows immediately upon discovering the scent which direction to move - even days after the track has been laid. They would have ignored the "back track" (that is where Jackie had been) and gone in the direction that he moved. Some dogs can be trained to back track, but this would be an exception because their instinct tells them to go forward.
It should be asked also if Jackie had been near that side of the Creamery or near the river at any time in the days prior to his disappearance. That might have tended to rule out the dog scent evidence if he had been there in recent days before he went missing.
The way that the map is numbered, would indicate that Jackie passed within a block of his house, then went to the river and then proceeded down the highway. That does not make much sense. I feel that it was more likely the other way around and that the 4:45 sighting was a case of mistaken memory, mistaken identity, or simply not true. Again, perhaps locating either or both of the boys who reported this might yield a different story today.
Concerning people with learning disabilities serving in the Navy or other branches of the service... The story did not indicate that Jackie was in any way severely retarded, only that he might have been "a little slow". There are many men and women serving in our armed forces today and in the past who have various learning disabilities. I do not mean at all any disrespect by that, only that it might be quite possible for Jackie to have served in the Navy if he had passed the entrance exams with acceptable scores.
I have no idea who the teacher in question was or why he or she did not ask the obvious questions. I wonder if it might be just more of the legends generated by the mystery of the story. With some specifics as to where the home port was, or what the name of the ship was, the Naval Historical Center at the Washington (DC) Navy Yard, or the National Archives at Suitland, MD, or the National Personnel Records Center at St. Louis, MO might be able to confirm the existence of a sailor named Jackie Theel in 1960.
It would certainly be good literary writing to have this lost little boy dressed in a sailor suit, later become a world traveled sailor. By the way, sailors were often referred to in olden days as "Jack Tars" or simply as "Jackies". In the early 20th Century, boys bands were often outfitted in sailor suits and referred to as "Jackie Bands". And even today, the sailor uniform with bell bottom, button fly trousers, jumper top, and square knot tie are referred to as "Cracker Jacks".