1) if you don't want it to snap, I'd go with high density furniture foam. It is sold at larger fabric stores. To glue it, use 3M spray adhesive. It's smelly slightly messy stuff, use it outside.
2) Yeah, probably wise. It's easiest to embed the pipe by building thin layers of foam around it instead of trying to cut hemispheres out of singular large chunks of foam. Round the ends of the pipe so it isn't a square edge. Don't extend the pipe to the ends of the cross. Leave like 3 or 4 inches of solid foam on the ends. Before gluing on the last layer of foam, spray in some polyurethane expanding foam (not too much) to lock the pipe in place. Leave the ends of the top layer unglued in a way that gives the overflow an escape route. If the expanding foam starts to push up at the sheet foam, push it back down manually. Trim away the excess foam, and glue down the ends.
3) nah. The finished product should weigh less than 10 pounds. Backpackers hike all over Europe with 100 pounds strapped to their back.