Re: First trip
Yes, I agree, that is interesting and confusing in the US, as well. I haven't done the research, but I've often heard that the rules about waterways and about the ocean aren't the same as for other places. That said, though, there certainly are parks in Michigan, for example, that don't allow picking up rocks from the lake. Collecting in Pictured Rocks National Lakeshore is off limits, for example. Many, if not most, of the Michigan state parks seem to allow collecting. Along the ocean, in California collecting isn't allowed on the state beaches, but I've often heard that picking up rocks along the ocean was legal as long as you are below the high tide line. Rivers and creeks are confusing, too. Supposedly if you are in a creek or river and you can access it from a non-private area, you then can legally walk in the creek even though it crosses private property and collect from said creek. This is an issue often in Kentucky, where the creeks are good sites for collecting geodes but it is really hard to gain access to the creeks without trespassing.
All of which suggests a couple of things: first, it's probably a better idea to go on a field trip with a recognized club if you can, and second, when in doubt about the status of the land, always err on the side of caution and don't go there if there's any question that it might be private property or a closed area. If you make a mistake you might get shot or arrested, neither of which make for a great RV trip!