When a new sorcery style is learned, the scholar learns the
Basic spell from that style and no others.
For Hypnotism it's Entrance, For Divinations it's Astrological Prediction, etc.
Advanced spells are any spells that are not "Basic"
When the scholar earns an Advanced spell, he may choose a new spell from one of the styles that he knows (or have one chosen for him, depending on his background)
You should make a thorough reading of the Scholar class section to get more details -- a scholar's background has a lot of bearing on the type of sorcerer he is and the types of spells available to him.
How does he gain bonus spells ... if he only qualifies for a limited number of spells in a style?
It sounds like you're confusing the bonus spells earned for having a high Int with the spells automatically granted by the class. Bonus spells earned for a high int are gained seperately from from those provided by his class. Also, it's possible for a high int scholar to have a bonus spell owed to him that cannot be fulfilled because he doesn't mee the prereqs for any.