This can all be determined by observing the steps of a Move.
1. Declare Move
2. Pay Costs
3. Leaving Zone Effects
4. Walls
5. Move
6. Entering Zone Effects
The key steps here are 3, 4, and 6. Well, currently I don't think there are any Leaving Zone Effects, at least none that come to mind, but it is potentially a key step. If the flyer loses flying before step 3, then it will be subjected to any Leaving Zone Effects that affect non-Flyers. If it loses flying before step 4, then it will encounter a wall and thus either suffer a Passage Attack or be forced to cancel the move. If it loses flying before step 6 then it will be subjected to any Entering Zone Effects that affect non-Flyers.
So, that should answer your questions. Walls obviously are encountered in step 4, while everything else you mentioned (traps, Bed of Urchins, and Mangler Caltrops) happen during step 6.
With regards to the Sherean Leviathan and Gravikor, your creature changes which zone it's in during step 5 and immediately stops being affected by previous zone effects and immediately begins being affected by the new zones effects. So, if the new zone causes it to lose flying, this is when it would happen, meaning it will be subjected to all Entering Zone Effects during step 6.
The Hydrothermal Vent question is interesting as it causes you to lose Flying during the Entering Zone Effects step rather than before it. Since the Entering Zone Effects step is still in progress though, you will still have to resolve any such effects that exist. Meaning, that if you lose flying, you will become a valid target for any Entering Zone Effects that target non-Flyers and be subjected to them. Hydrothermal Vent can cause you to suffer from Bed of Urchins etc.
I hope that clears things up.