Fast Mana regen is gone and will not come back, at least not the way it was once used. It is possible that the general idea may come back at some point in another way, but at the moment, the fastest way to regenerate mana is through potions. In the new area of Ryze, Yellow Sand is for sale. A yellow potion will give you 20 mana. In case you are unaware, you can drink unlimited potions now. There is, however, a time limit on them. You have to wait roughly 6 seconds before you can drink another.

As for leveling mage skills, nothing helps them level faster. They are leveled randomly.