Use green screen & some fast isolation software, such as those from FXHome - the older PhotoKey or the new Imerge (which I haven't tried yet, but seems to also be half the price of the old one.)
Other solutions are available, but that's the one I've used the most. Googling for stills software isn't as easy as for movie, but it's out there somewhere. I ...
Open it in Adobe Camera Raw. There are several ways to do it. One is from Filter menu | Camera Raw filter.
Press Shift+T in order to activate the Transform tool. There you have several modes from which one is Automatic (the 1st one) and Guided aka. Manual (the last one).
Also, you can play with the sliders. I didn't target for perfection but here is a ...
Because you did not also increase the chroma contrast. As a 1st order approximation the perceived saturation goes with the chroma : luma ratio, best kept constant.
No, that would be due the Hunt effect, and it is a matter of human color appearance versus simplified math.