I can see the reason the duct work hugs the joist, is because the hot PEX line wouldn't allow the HVAC duct to be centered like the rest. I don't know why they ran the PEX the way they did based on the one picture.
No the duct does not need to be insulated, the basement is conditioned space. As far as return air in the basement at least in the areas where I build, there are various code issues with return air in an un-finished basement, that might be the case depending on your AHJ as well.
I see you are in Indiana, I am in Colorado where we cannot even find a dehumidifier in a store (we don't need it, were dry here) but in Indiana its a must. I know of at least 3 houses that had fires in Ohio from cheap Home Depot / Lowes / Menards dehumidifiers over the past few years, so I might suggest you talk to an HVAC company and have a whole house dehumidifier installed as opposed to the cheap, free standing units; because depending on the size of your basement you might need more then 1 free standing, and for a few hundred more you could get one installed with a rock solid warranty and one that is more efficient.
Congrats on the new home.