Bottom hat tilted toward me about 1/4 inch (6 mm) lower than the back. When at rest, the back of the hats are about 3/4 inch (20 mm) apart; with my foot on the pedal, that distance closes to about 3/8 inch (10 mm) in the back.
With that arrangement the hats can chick, sizzle, bark and splash just fine (though not at the same time!).
I like enough space that they don't touch when the pedal is up. My criteria for adjusting that space is done with consideration of how far I want my left ankle bent when the cymbals are
open. I also like the top cymbal on loosely so it is floppy with the adjustment screw tilting it
Very little space - just enough so if I have no foot on the hi-hat pedal, there's half to maybe three-quarters of an inch of space, and the top hat isn't stiff in the clutch. I prefer a slightly washy open sound so I rarely play them wide-open; in general I don't like the clangy sound that seems to result. That being said, I've never recorded myself playing them that way - it might sound better "from the outside" than I think. Something new to try!
Depends on the song I'm playing. If the song has either an open or closed hat sound for the majority, I pre-adjust the hats to be more open or closed accordingly beforehand. Sometimes distinctly separated, sometimes lightly touching. I find that it reduces the amount of focus and effort necessary for my left foot to operate them as needed. On average though, I'd say they're rarely farther apart than 1/8".
Probably 1/8" to 3/16". Playing double kick I will sometimes keep my left foot on both pedals so I can get some accent work going, and other times I will just let them slosh. When only playing single kick I usually bounce my foot on the pedal. I don't remember if this is why I keep them so close, but I found out very early on I don't like them wide open.
When open, the air ranges from around 1/3" on the tilt side to 1.5" on the open side. Top hat quite loose and clutch? tension is fairly tight, so it doesn't take much effort to open/close.
heavier K Custom dark hats.
About 1.5 inches (4 cm), a slight tilt with a medium spring adjustment, the footboard angle is the same as the bass drum pedal. It's a 13" K/Z combination, so the bottom cymbal is fairly heavy and the top is medium weight.