Hey, sorry, I was working on answering this and then got sidetracked and didn't get back to it. Your idea is really good! Hopefully these answers will help you out:
1 & 2: The major way of getting between fog-free pockets where cities are is to travel through clear routes called "dungeons," which are usually underground passages. There's lots of these, both large dungeons that are widely used and small ones that are hard to find and difficult to pass through. Time and space inside dungeons is kind of weird; the paths change, and there's all sorts of weird phenomena, but you can also pass through them much faster than just walking on the outside.
Flying pokemon can also fly above the fog, but this is only really feasible for those who can fly at very high speeds or for very long distances without tiring, since it can involve flying dozens or hundreds of miles.
3: Explorers do a lot of scouting dungeons and making them safe for travel, and helping guide/transport other pokemon would certainly be up their alley. The Hunters also do a lot of dungeon delving, and also transporting sensitive materials or escorting important folks. A courier team would fit in with either of them. And if you really wanted to make a Researchers team, they could specialize in helping scholars travel to and from research sites, say.
4: There are and will be events involving transportation. In fact one of the Hunters tasks from the Basalt Halls dungeon is an escort job, and one of the Explorers tasks from the Cactus Fields involves rescuing lost pokemon and bringing them to safety (you can still do both of these for merits/strikes and partial rewards).
5: You'd need to pay or use vouchers (obtainable as a bonus from Mission 1) to modify your team's accessories.
Hope this was useful. Sorry again for the late reply.
Most big events give you the opportunity to pick up at least some star coins, and sometimes other rewards, if you do them late. For example, you can still get 2 star coins from doing M1 late - not to mention the vouchers if you complete the bonus objectives, which help a lot with customization costs.