That does make what you are experiencing less improbable. Cloth rim strips are usually helpful on double-wall rims, as they bridge over the access holes for the nipples better than anything stretchy. But they won't be anywhere near as "special" on a single-wall rim, what you need there is basically padding to cover the nipples.

As it's a bike bought new from a dealer it's really his problem, and he should be able to sort it out. Some things comes to mind though, maybe the wheel is built with slightly overlong spokes? that would have the ends of the spokes poking through the nipples causing pointy nubs. If this is the case one can either rebuild the wheel with slightly shorter spokes, do a bug-ugly fix and stick a washer under every nipple or simply grind off the protruding nub of each spoke. The latter is almost as bug-ugly as the washers(but faster with an angle grinder) as it might have to be repeated if the wheel has to be trued/re-tensioned, but still a doable solution.

Not likely. First off rims do vary in width, and I've never heard of that causing a problem for the tube before. Secondly, the tube has almost zero structural integrity in itself, it'll simply stretch to fill whatever space there's available for it.

What one would first think of in that case is a burr somewhere that'd be poking holes in the tube, which either you or the dealer ought to have spotted by now. Possible, but very unlikely is that your rims is a tad off spec, which allows for more spoke protrusion than otherwise.