Any chance your brakes have been rubbing?

Hopefully the photos you sent the manufacture were better than the ones above.

A little age checking doesn't seem to be that bad, but is up to the rider. However new tires, with cracking near the bead is concerning. The cords, of course are what give the tire strength, but the integrity of the cords is difficult to assess under the rubber.

I'd probably toss a spare tire in my pack, and continue riding. However, I suppose it depends on whether your riding is such that a flat or blowout would be catastrophic. Group rides? Long distance tours?