Phil, welcome to the forum.
Here are some additional responses to the numbered items in your mega-question 🙂:
1) Foam. The plans specify the foam to use.
2) Alternates to foams. Not worth the consideration in my opinion. I wouldn't even consider changing the foam material as the cost/effort-benefit would not be worth it.
3) MTOW vs Max Ramp Weight (and Max Taxi Weight). I just learned something trying to figure out what these two new MRW and MTW terms were. Most (all?) small airplanes only care about MTOW as the maximum weight the aircraft can be, whether in the hangar, or about to take off. I have never seen someone thinking about subtracting the 1 pound of fuel they might have burned from the hangar to the runway.
4) Round the World. Nobody is going to give you meaningful and specific advice on how to plan a round-the-world trip in a public forum, so expect that. Be prepared to deploy all your cash reserves here. Get in touch with Damon Meyer who was planning to do the same in his flying Cozy III, which he had fitted with a huge fuel tank occupying his entire back seat. After years of planning, campaigning, and real work, he has not been able to get off the ground though. It's a massive undertaking.
5) The Cozy plans include the Roncz canard plans (modified for the Cozy).
6) Engines... round-the-world... diesels... turbines... oh my. Build a Cozy IV with a Lycoming 360-type, take yourself to some places, and then your family when you trust everything. It's massive accomplishment considering the success rate of those intending to build and fly vs. those that actually do it. Once you've built and flown in standard configuration, look at your plane and revisit whether it's the one to fly around the world. At that point you will know enough to answer your own questions here.
Your first step is to buy the plans.