Do not lift throttle abruptly in a turn. That will induce 'trailing throttle oversteer', and possibly spin the car.
You are doing it right by learning on street tires. The squealing is good, do not be afraid of that. (be afraid of the car and your ability to handle it)
Race compound tires don't communicate like that, so stay with the street tires until you've had some instruction, and are 99% confident in your ability.
(That last 1% of doubt is what will keep you from killing yourself. -the minute you think you are 100% in control of a Viper, that's when the car will teach you otherwise.....don't ask how I know.)
Street tires will squeal when getting into the desired 'slip angle'. That is the limit of usable traction for the given tire. -Right before it's gone, and just a little before that. Thats where you want to be. Street tires are great for learning because of all that noise. Listen to it carefully and pay attention to it. The subtle nuances of the tires communicating with you, about where they are in traction, or lack of it. A nice steady constant, non-varying, tire squeal is your goal. Varying degrees of intensity while you are sawing at the wheel, and up and down on the throttle is bad. Slow, steady, smooth inputs to the car will get you through the corners quick without incident. Also driving the proper line will help. If you have no idea what 'the line' is, like others have said, get an instructor.
Vipers require skilled handlers to be driven fast on a track. And that's what makes them so rewarding. There are some other cars that are fast, and maybe faster than yours, (modded,non-street legal, whatever) but the driving experience of a Viper at the limit is like no other.
Again, the squealing is a tool to help you learn. Not a bad thing. If you change brand of tires, they will squeal differently, and you will have to 'learn their language'. If you put R-comp tires on the car, you will have to depend on skill and a 'higher developed sense' of where the limit is, because R-comps don't talk. -A new sense of fear......don't ask how I know.
Enjoy the car, and your new found addiction, be safe.
-Allan