Hi there, and welcome! Always nice to have another kiwi around!
I can't comment relative to the K10, as I don't have one, but when I upgraded from my K100 pretty much everything was better. That's not strictly a fair comparison, given that the K20 is much newer, and a more expensive camera, but that's how it is.
Yes, the mirror slap on the K20 was/is quieter than a K100. Can't compare to a K10 though. Liveview on the K20 has been of extremely limited use for me, I've mainly only used it when holding the camera overhead. It's important to note that when in liveview, it has to disable liveview, lower the mirror, focus, and then raise the mirror and reactivate liveview in order to autofocus. This translates to maybe a second of blackout of the LCD.
It's possible, depending on where in the country you are, that you might be able to meet up with someone and try a K20. Or, if you're in Auckland, I know of a couple of shops which have them on the shelves.
By the way, there is an ongoing thread many of the kiwi members post in, you might like to introduce yourself there:
https://www.pentaxforums.com/forums/everything-else/41021-kiwi-pentaxians-25.html