What effect do difficulty levels have

Like you said, Set items get carried over along with the dynasty weapon and some plot items (Anastasia's comb). All the other items regularly appear across missions (Just how many helms did Sandro make?!).

Some towns are limited in terms of what they can build and how far they can upgrade. This is just part of the setup of the scenario. I'm not aware of any way to tell what these limitations are prior to capturing the town.

Per chance are you in the second part of the tutorial campaign? The forts in that mission can't be upgraded with any recruiting buildings. But the first town that you take (the one directly south of your capital) can, as can the necropolis town controlled by the green units. Better yet, if you convert them to your faction, you can recruit all of your units from them, even the ones that are being "produced" in your capital. This makes for much less walking around to collect units. You can also use a secondary hero to go back to town, recruit units, and then deliver them to your primary hero.