How does magic influence society? Who learns it? Can anyone learn? What about the poor people who can't even read? Can they learn? ?
Inborn: Magic is entirely inborn and is generally only taught by a mage after one has gained basic control and they find you (or you find them) and they explain what they know. It's purely democratic and basically picks people at random as far as most can tell.
Learned: Only the nobility can learn this, or those they sponsor. Poor people cna pick some up from listening to mages, but they're always given a lot of disinformation along with it. The poor will never learn magic. It's not sanitary.
How is it learned? How does the common person feel about his son learning magic? What about an aristocrat? ?
Inborn: No one wants their child to have magic. Parents suspecting children of magic have been known to drug and then blind them or cut their hands off or their tongue out, to be on the safe side. (This doesn't work, but it is done anyway.) Killing a mage of this kind is generally a very dangerous undertaking since the magic will act to protect itself.
Learned: College teaches this magic, and the common person won't have a son learning it but could have a former child now a minor noble and will never associate with scum like you again most likely. Nobles like their sons to learn magic, if they have no aptitude for the sword or diplomacy or the like. If the family has no mage for whatever reason, they will force it on someone. Most families like to have 2-3 mages, and 3-5 in apprenticeships. Lesser families share mages. Having none is a serious status blow.
Go through the daily life of a peon with emphasis on the parts of his life that are influenced by magic. Does he use a magic axe? Does his wife clean the kitchen with a spell? How does he feel about magic users? ?
The average peon has as little to do with magic as possible. Learned mages tend to be consulted by villages paying a fee for divinations and the like, and Inborn ones are consulted by being asked to do something, and then told to go away.
Are magic users respected, feared, or treated like engineers? ?
Inborn: Feared, pitied, derided.
Learned: Respected for rank as much as anything, and often treated like engineers and somewhat lesser than other family members.
How influential are magic users?
Inborn:
Learned: Very, since they do divinations, but aside from that they're not powerful enough to wield much influence and ties among them are a) family b) college. Other mages are looked upon with distrust or envy often enough.
What kinds of magic are there? How is each treated? How common are they?
The only kinds of magic are inborn and learned. Inborn magic is rare and some of them get captured by Learned mages and used as a power source and die anyway. Mind you, most learned mages who try this fail
Learned magic is very common among nobility and treated as a specialized skill.
There are no holy magics in this setting, no gods wielding healing spells and the like. (A witchcraft version of magic standing between Inborn and Learned does exist as the Village Wise Woman/Barbarian Shaman but it's not that common. Many of these tend to be captured by Learned mages seeking Inborn ones.)
Why do people bother to learn/develop magic anyway?
Inborn: They master it or it masters them.
Learned: Something to do, have no choice, ordered, or it's the only thing they're good for.
How does society/mages police magic users? Are their laws regarding how/when it can be used? Spells that are illegal to learn/teach?
Inborn: They are generally hunted down by terrified mobs or live as hermits. Use of this magic is illegal in cities and in the country in general.
Learned: The college keeps a careful eye on mages and the infighting and back stabbing tends to prevent excesses. There are no illegal spells (since few are actually powerful) but some are frowned upon, such as necromatic stuff. Learned magic is used in the cities at will, though it can only be used in the demesne of nobility (even ones own family) with express permission of said family.
Are there dangers inherent in magic use?
Inborn: Using magic is fatal unless one is awfully lucky.
Learned: Using real magic without the proper rituals is fatal.
Some final thoughts:
Inborn magic is very high-powered but rare. Learned is common but rather weak (it does have the advantage of being more versatile but at the cost of taking a long time to do anything useful). The Witchcraft/Shaman variant straddles the line between the two and is basically a self-taught learned style with more emphasis on real magic. It's rare since often the teacher is unable to find a pupil or runs afoul of the authorities.
A divine(?) magic system acting more as psychic powers and used to ferret out and destroy Inborn mages could be added as well. It wouldn't have healing magics, though, since those tend to unbalance a world a lot and exist mostly to keep characters alive when their own stupidity should have killed them.