When I can find the right trade, I use lightweight steel framing in the basement. Fast and neat. There are a couple of situations where wood is combined with the steel for door attachment. Otherwise, no, you don't mix the two.

On your pic, I don't see how the studs are attached to the baseplate. I see one screwhead on the third stud from the left. None at the top of the studs. Let alone, how is the topplate even attached to anything. I suppose once they jam in the drywall, it will all stay together somehow.

Grommets for use in light metal framing.

The wires through the topplate must be protected by grommets. One is clearly not--it's jammed between the plate and the ductwork. There's another four that may or may not be simply pushed through a hole made into the topplate.

In the first picture, there are cables running on the outside of the plate. You must not pinch wires between framing and the drywall!

Hopefully, this was permitted work yet to be inspected by your local electrical authority. It takes just one wiring fault to cause a fire.

You can clearly see the Romex connectors through the metal stud in the first picture.

Steel studs are 3-5/8", wood are 3-1/2". I've not seen this done.

It's a small partition wall. I wouldn't lose any sleep over it.

You can clearly see the Romex connectors through the metal stud in the first picture.

Yes.

I was referring to the second picture at the left.

Clearly, I'm too picky. As a framing carpenter explained when I noted he left half the holes in hangers without nails, "None of my houses have fallen down!"

Off topic: I've never seen an electrician loop Romex like that. Must not use pigtails in the boxes.