Other than the obvious improvements you will see when you get into SB VS. BB situations, I think overall you are going to find that you will get more comfortable in the situations where you are playing wide ranges vs. wide ranges. Stuff like BB vs BTN and BB vs CO and SB vs BTN and SB vs CO.

The dynamic is so much different in blind vs. UTG and MP opens since both ranges are more sung and linear.

However, I think the combination of playing any game + studying is going to make you progress no matter the format.

1) I'm going to start playing HU cash, too.

2) I also play Chess and am USCF. For a while, I had an internal conflict about devoting time to two games but after a while I realized that's silly since so many players of one game do play the other. Then I started to see how much playing and studying Chess helped my overall thought process at the poker tables and now I'm playing both games. Of course, with a massive priority on poker since that's what makes money.

For sure. The most common spots in 6max holdem are CO - BB, BTN - BB, SB - BB.
These spots require skills playing wider ranges. So if you are a god at heads up you definitely profit in 6max as well.

Yes. Playing HU from time to time has helped my game a lot. I am able to hold my own in starting 6max tables and getting to play HU vs weak players before table fills up are adding a lot to my winrate. You are also putting yourself in a ton of spots in a short timespan so you will be able to learn a lot in a short timespan if you do the work. GL!