While this is horses and stable doors, it's generally better to buy a better case with better airflow and more/better fans than to buy a cheap case and then add extra fans.
Is the noise obnoxious? There's no problem with running them at full speed on idle, it just means lower idle temps.
That said, again, if it was an ultra quiet system you were after you should have bought a different and better case - and possibly other different components too, depending what else is in there.
The thing with fan splitters is that you can only chain so many fans off a single motherboard header, until you get to a point of drawing too much power. Two fans are probably fine but tbh I'd probably consider getting a powered adapter anyway, especially if there's a chance you might add even moar fans.
Make sure your Noctua fans are actually the PWM versions or else they won't be PWM controlled.
Why replace the rear fan? Again it sounds like sinking yet more cash into the case where you should have just bought a better one if you wanted improved cooling. Also if your replacement one is 3 pin it's not going to be PWM controlled either. As for wanting a specifically short cable, you'd normally just route the cable to hide it. Especially if you are getting a splitter type cable where only 1 cable for all your fans leads to the motherboard.