No idea. I think a lot of bike makers will have some "non-racing" ones, and also racing ones that won't do. I'd go to a few bike shops, look around, and see what appeals to you. Since you're not thinking of getting a new bike for a while, now is the perfect time to be thinking about it, and looking at lots of different options.

Well, no, but that might be a good idea, too.

Road bikes tend to have narrow forks and rear triangles, which means they don't have clearance for very wide tires. A lot of the ones meant for racing are limited to something like 25 or 28 mm. This might be perfectly fine - you're talking about MUPs and roads, where skinny tires make you faster. But it might not. Fat tires are more comfy, like shock absorbers, better in gravel, and might be better for touring. Also, it's pretty common not to have anything to mount racks, fenders, and the like to. My Cervelo RS accepts two bottle cages, and whatever I'd like to clip to the handlebars. There are non-racing road bikes that will let you mount stuff easily, but again, I'm not sure which ones.

"Relaxed geometry" basically means the handlebars come raised up a lot, so that you don't have to bend down as much. That might be a very good thing, but don't expect that all bikes in this category are going to be ready for touring.