The spare tire is up against the undercarriage toward the rear of the trailer. Nearly directly beneath the garage. There is a lowering crank device on the curb side located behind the rear axle and before the back steps. This is similar to the spare set up under the bed of most full size pick-ups. The trailer might have a spare up there but at any rate, I believe the mechanism is standard equipment.
You're correct on the age of the tires. They are two years old so probably old stock as you suggest.
You don't need the water running to smell the black tank. Just open the toilet valve with the water off. If nothing major or overwhelming comes through you should be good. I noticed you are in VA so with the freezing temps you might not be able to smell anything anyway.
There are/were a couple of people on this forum that happily full time in this rig. We don't but one of the drawbacks for us when we're out for weeks at a time is there are no decent outdoor viewing windows on the curb side or back as you might see on more residential floorplans. We replaced the couch with two powered recliners pretty early on but there isn't much of a view unless the entry door is open. I took the screen door to a local glass shop and had them cut two Lexan panes that fit inside the lip on the top and bottom of the screen door(screen still in) I can quickly install so we can leave it open when it's brisk. My wife really likes that modification.