Tires during storage

When I bought new tires this spring the dealer told me to block up the trailer to keep the tires from squatting all winter, FWIW he also said that the best thing to do was take them off and put them in the basement.
I blocked it up but it's a hassle.

No, but it is a good idea to cover them for UV protection. Also put something under tires if they will sink and so sit in a puddle.

I leave my stabilizers down as it helps, duh, stabilize, when we get high winds.

Over 200,000 miles on various non-Chinese ST tires, and only issues have been a few repairable nail punctures.

As Latner just said above, make sure the air pressure is at maximum...slightly over wouldn't hurt actually. Also, don't use the stabilizers. If the tire pressure does drop over the winter or the ground sinks slightly, there would be excessive pressure on the stabilizers and damage could occur. Also, again like Latner said, cover them if they're outside because of the sun.

No. My trailer sits outside all year on a concrete pad with no issues. Keep the air pressure up and covered if exposed to the sun.