Yes a toolhead cover will come with one.
I can’t answer your other questions but if you decide to dyi you’ll have to splice the connector onto the new fan.
If I were a betting man, I’d look for a replacement that matches specs of the original.
So I ordered another toohead cover, it came with the 0.22amp Snowfan, I compared the two fans with these instruments (+ a cellphone dB app, held at the door of the printer) here’s the results, maybe 7 percent better, and 8dB quieter.