Disclaimer.... I have not built an entire foamie, but I did some testing for a foamie project I have planned for spring. Regarding your questions:
1. Best thing I have found is a "collapsing Polyurethane foam" adhesive. It's a general construction adhesive, but works very well on foam tests I did. Great Stuff makes some, but you need a special gun to use it. I have used Tremco, because you do not need any special gun.
https://tinyurl.com/2csdd82m
2. Same Adhesive as above.
3. Use a trim router to cut organized grooves only to the depth you need them. Fill with an expanding foam and saw off the excess. But plan ahead if you do not want that one wire you forgot to be exposed. Run the router along a guide for nice straight lines.
4. Over the years of reading, I have heard of people having their trailers blown sideways in side winds, even flipped over. That said, I followed a fellow for 7 miles in a snow storm who was towing a regular 6 x 12 single axle cargo trailer in a snow storm with high side winds. The trailer was sliding 90 degrees along side of him the whole way on the slippery road. CRAZY to watch, but there was nothing he could do. I'd like to think the thing was empty, but it shows that anything with a large side exposure can be a problem with side winds.
The good news is that because you have such a light trailer, you can carry a lot of water and gear to make up for the difference ! Kind of defeats the purpose, but seriously, there are obvious some tradeoffs with being really "light".