Welcome to the fold! IPSC is an absolutely fantastic shooting game. Just of note, you asked about IPSC, but if you are in the US, you will shoot USPSA instead of IPSC...though most of us call it IPSC (USPSA is the US division of the international IPSC organization). The games are identical, but there are some very minor rule differences in spots.
#1 How do you get classified and why so many times
USPSA has a 'classifier book' with courses of fire that are used at clubs across the country - it ensures that everyone sets up the stage exactly the same. At the local level, it is customary to have 1 course of fire that is a 'classifier', so if you are in the game for a few years, you'll end up with lots of classification scores. Look at this page for more info
http://www.uspsa.org/dw/whatis.html#Classification
#2 How do you excel? Meaning shoot as fast as you can while still trying to get "A" hits.
Shoot as 'fast as you can see' the sights return to the target. Those that excel in this game have mastered this, and have eliminated/minimized the amount of wasted movements between targets (either in transitioning between targets, or in getting from position to position on a course of fire).
#3 Can you shoot both stock and open divisions?
Yes, but usually not in the same match. USPSA has 5 separate 'equipment' divisions. Check them out here...
http://www.uspsa.org/dw/whatis.html.
#4 What would be you best caliber, I have a .38 Super Bianchi gun.
Answer to this depends upon which division you decide to play in. I think the most common caliber in each division is: Open-.38super, Limited-.40, Limited 10-.40, Production-9mm, Revolver-.45acp.
#5 What type of practice should I do, Bill drills, double tab at targets of various ditances, etc?
There are several good books out there with lots of drills. I suggest the Saul Kirch books, Perfect Practice (tons of drills), and Thinking Practical Shooting (game concepts, match management). Each drill is designed to help you learn about certain aspects of your shooting. Very good material in both of these books. Both of these are available from uspsa.com webstore.