If I am playing at, say Apprentice skill level, (hey, I am 68 years old!) and change to a higher level before opening a chest, will that change "usefullness" (for want of a better word) of what I may find in the chest?

I.... don't have any idea. Hey! You're even older than I am! *laughing*

Pretty sure you find the same stuff at all difficulty levels.

Just figured it out by myself by experimenting. Same stuff, any level

Yeah, I think that's the case. I play on Adept and I haven't seen anyone who plays on Master refer to any super item that I haven't seen in my games.

Changing the difficulty won't change the contents of the chest but leveling up will.

Loot, as with baddies, are set compared to your character's level when you enter a location. If you're level 10 the loot and enemies will be set accordingly. So, if you're having trouble with battling in a location you can leave, level-up, and go back later or you can move the difficulty slider down in the options. Either works.

Yeah, that's what I noticed when I stepped up to expert (and later master) because my character power grew faster than that of leveled enemies. I'm back down to expert now, but considering master again. Power crafting (even without any exploits) is just that good.