This is all Legends (the games in and the books they are loosely based on).
Yes. He taught the traditional Form IV.
Because Luke was trained in Form IV (also know as Ataru) by Yoda, he did instruct the new generation of students in this form. However, this form didn't work for all scenarios, so with the assistance of others, they developed the Strong, Fast, and Medium forms.
While Luke had been provided with formal training in Ataru by Master Yoda, passing this on to his own students, the loss of so much knowledge from the old Jedi Order, including many lightsaber combat techniques, forced Luke's new order to essentially start from scratch. Kam Solusar trained the students in the three rings of defense, while Corran Horn trained them in many of CorSec's combat techniques. The three forms of the Jedi Order were eventually created, each specializing in a different aspect of combat. The Strong style focused on brute strength and offense, often at the expense of defense. The Fast style focused on speed and precision, and was especially good for blast-deflection. The Medium style balanced out between the previous two, and oftentimes acted as a tutorial form, much like Shii-Cho for the old Jedi Order. - Wookieepedia- Lightsaber Combat
He received only the simplist instruction in Form I (Shii-Cho) from Obi-Wan Kenobi citation.
Eventually (after the events of the game) all forms were apparently rediscovered (according to the previous citation).
Shii-Cho, like the other six forms, would eventually be rediscovered by the New Jedi Order