Welcome to the forum. On your second post, I wouldn't want that much stuff at the top of my tree, but if it works for you, go right ahead. With that being said, what's the point of the three new planes? You already have the three default planes, so why do you need more? And I rarely want planes viewable, but that's just my preference. I like a clean graphics area, without visible planes and sketches cluttering it up. If I want to dimension to planes, or use them to establish a relation, I select them from the tree.
I do have three axes a up in my Assembly template (one each at the intersection of the three default planes), but they aren't visible. I use them to define the direction for linear patterns, and occasionally as the axis for circular patterns. Again, I select them from the tree, so there's never a need to make them visible.
1) When you set up a new plane, there is an option to "flip normal". This affects which way is "up" when you right click on a plane and select the new sketch icon. So try that on your ZY, XZ & YX planes.
(Flip Normal is not an option with the default planes.)
2) Go to Customize and select the Keyboard tab. Here you can find the command you want and enter your own shortcut. So in theory you could set up your copy of SolidWorks to run with NX shortcuts.
3) Like Glen, I usually select my planes & other reference geometry from the feature tree. I like to use that double arrow >> at the top of the feature tree to show the visibility column. This way I can quickly show or hide anything in the feature tree.
After 13 years with SWx, currently I'm using NX at work (Switch to another company using NX)
1) In SWx I did the same Z-up but had to switch back to default system because of the downstream operations are based on SWx defaults. It' was much easier to change my way of visualizing so that Machinists didn't have to rotate parts in their CAM programs. For SWX Parts, just think that SWx Front view = Model's Plan view = XY plane = screen and Z is towards you. Or the Screen is in horizontal plane. But for SWx Assemblies you could reorient the views as you like(Cam programs couldn’t open SWx Assembly files)
2) Press the Spacebar then you will see a Cubical block and click any face that you want to be on your screen like NX's F8.
3) If you look closer, there are 3Planes and origin point in every Part file as a default. RMB them and select Show. If you like change the templates too.