1+2. They consider necromancy a taboo art, which is probably the only thing they and Aefenglom have in common. While it isn't against the law to practice it the way it may be elsewhere (though understood You Really Shouldn't), the Coven has made it terribly hard for one to find any information regarding it at all - even more than Aefenglom's has.
3. Only those with more focus on divination, manipulation, and enchantment spells... easier for people to learn so anyone, regardless of education, can know how to control their Monsters.