It looks like rain water got in back of the siding, ran down the sheathing and out the bottom. I'd be looking for where the rain got back there.

They may have forgotten to install a kick flashing behind the siding where the roof meets the gutter. Without the flashing water will run down behind your new siding and come out right where the stains are.

Probably, also not the best place for a planting bed. Its running down the foundation there, too, and causing it to not look so great.

This is directly on the inside of the house. It hasn’t rained in a few days and is still dripping inside. The ductwork feels like it’s leaking air when the a/c is on. The walls have no insulation in the wall cavity. Could this be condensation in the wall? I fear the leaky ductwork might have been during siding installation where perhaps missed nails through the wall hit the ductwork.

Time to call an HVAC guy, to inspect your ducting, and repair it.