The latter problem is easy to fix on a per-window basis: You just hit the "full screen" buttat at the window's upper left (the pale green button third from the left). This scales the document to be really huge, with a scroll bar at the right, but it also shrinks the window vertically to fit on the screen. You can then grab the resize button on the lower right and change the window to a good size for what you're doing. But this doesn't do anything about the window's startup size, and the problem will recur the next time you open a new Preview window.
What I've found works is something that's not at all obvious from what's on the screen. If you use the Preview -> Preferences menu item, and click on "PDF", it shows you some settings whose meaning may be a bit myseterious. Usually "Auto-scale" is checked, and this seems to be what causes the problem. It seems to mean "Scale the window so that it's far too big to read on your screen." If you try un-checking "Auto-scale", it doesn't work, but that's because it and the "Use scale of" button are a pair of "radio buttons". If you click on the "Use scale of" button, the "Auto-scale" button will turn off, and you can enter a number into the settings little input widget (before the '%'). I've found that a setting of 70 works well for most of my uses, giving a window height of about 80% of my screen. But I had to experiment, because the number seems to have no obvious relation to either the screen height or the document's physical (printed) height. You'll probably want a different number.
If I ever learn what a "Greeking threshold" is, maybe I'll add something about it here. Experimenting with it didn't do anything that I could understand, and google didn't seem to know what it was, either.