Thickness of batter; about as thick as double cream. No lumps for choice, but small ones aren't critical.

Hotter oil will crisp the batter more quickly, and should be absorbed slightly less, thus marginally healthier. The trick as I see it is to balance the time at temperature so as to cook the fruit through, without overcooking the batter shell. Maybe tackle getting the batter mix/cooking right first, then increase or decrease the thickness of slice so that it is cooked how you prefer it.

I'm told there are thermometers with which you can be certain of the oil temp, but deep frying is something I seldom do these days.

BTW, I didn't answer about pans before, saucepan for me, I don't think I have ever had success using a frying pan for battering food, though I did once use one to drive [batter] in tent pegs.