The normal temperatures that I have always housed a ball python at was 90-95 hot side, and 80- 85 cool side, you would set the thermostat to keep those temperatures. You don't really need a UV lamp since ball pythons are nocturnal, but you can keep it if you want, but ceramic heat emitters or red heat lights are best.

Drool coming out of the mouth is usually a upper respiratory infection, it can be caused by low temperatures, along with other things. You could bump the temperatures up a little with a hotter heat bulb, but don't bump the under the tank heat mat temperatures up, you would burn the poor snake.

Try to keep humidity at 50- 60% to ensure good shedding, it will help with the eyes, to me it just sounds like stuck eye caps from not being able to shed properly due to poor humidity.

If you need any other help just ask, and of course good luck.