I think these conclusions are accurate, but they are (of course) based on limited observations. Please correct anything that is wrong.
Dancers and musicians can start their "random" walks by teleporting several tiles from the pavilion. Musicians can start their walk to a pavilion by teleporting several tiles from the conservatory. But there are many questions. When do they teleport? Where do they appear? Can musicians teleport from a bandstand or from a conservatory when going to a bandstand? Can dancers teleport from a dance school? Can jugglers teleport? (The same or similar questions apply to other walkers, so they won't be repeated.)
Senet players can teleport back to the senet house at the end of their walk. It appears that when a senet player finishes the "random" part of his walk, he sometimes chooses a destination road tile that is several tiles away from the senet house. If there is a road connection to that tile, he walks there and then teleports to the senet house. If there isn't a road connection to that tile, he simply disappears.
Some other walkers (including architects) have been seen to disappear rather than walking back. It is possible that they are behaving like senet players--at the end of the "random" part of their walk they choose a road tile some distance from their building, walk there, and then "teleport" the rest of the way. This is pure speculation.
Bazaar traders can teleport in two different situations. One is the initial appearance of a trader from a bazaar--either when the bazaar first gets food (I don't know whether this can happen with an unevolved bazaar) or when the second trader appears after a functioning bazaar evolves. Since this kind of teleportation can only happen once, the effects (good or bad) are temporary.
The other situation where bazaar traders can teleport is when the two traders from an evolved bazaar appear at exactly the same time--one of them may teleport to a different road tile. At one point I thought of using this effect to supply food to another road, but it was too irregular--the interval between teleportations varied from a few months to almost two years. Luckily, it is often easy to not evolve a bazaar, which prevents this kind of teleporting bazaar trader from delivering food/goods to the wrong houses.