Settlements in F4 seem to have a lot in common with Fallout Shelter (supplying power, water, food, being able to equip dwellers with weapons and outfits, attracting others via radio). Can settlers "dance" and get pregnant? Do I need to build two beds together for this to happen, or equip people with clothing with charisma bonuses?

Uh, no.

How? Sure you can trade with them but I have yet to see any of my settlers use the weapons and armor i gave them.

Select the item in their inventory, and I believe use T to force them to equip it. Believe this works for companions also to replace their default outfits.