Can anyone become a wizard, or does one need to be born with some special talent or gift?
In theory, yes: anyone can become a master craftsman. Talent/aptitude comes into it a bit, but mostly it's a matter of discipline and focus, and the ability to be in love with the craft--as is true of mastery in our world.
Can you make a living practicing magic, or do you have to have independent means? If you can make a living, what are you doing — making magic swords, or making it rain for local farmers? What’s a wizard’s job market like? What’s a wizard’s average income, relative to the rest of society?
Well, craftsmen, so.... There's no crafting of weather. Income varies by skill and locale, and is usually family income, not individual.
Are magicians a force in politics, or are they above it? Are there national politics that revolve around magic/wizards (i.e., trying to outlaw, protect, or promote certain kinds of magic, trying to draft wizards into a ruler’s army, licensing of magicians, etc.)? Do wizards have a lobby? Do they need one?
Nopety-nope-nope. They're just regular folks and are treated as such, although as true master craftsmen tend to be old, they do get special weight in decision-making because of that.
Does it require a license to be a wizard? If so, is it more like a driver’s license (something nearly everyone in our culture gets upon coming of age) or like a doctor’s license (something only a small percentage of the population will ever get)? Who certifies wizards: government, wizard’s guild/AMA, local priests?
Nopety-nope-nope. Society in general doesn't have even the idea of licensing/certification. It's all very word-of-mouth, reputation-based. A matter of who you studied with and whether they think you're good enough to recommend.
How do local people view wizards? Are they good guys, bad guys, Clint Eastwood (call in only to get rid of dragons), regular working stiffs, ivory-tower academics, nuisances who make it rain when you’re plowing, dangerous folks to stay away from?
Regular working stiffs? Or Yo-Yo Ma/Shakespeare/Rembrandt. Only for making useful stuff that's also beautiful.
How do you get to be a wizard/magician? Does it require inborn talent, study and hard work, practice, or all of the above?
Pretty much all of the above, with the caveat that theoretically everyone has the inborn talent to become master of some craft or other.
Are wizards barred from certain kinds of government jobs or offices? Do some government jobs require that their holder be a wizard?
Nope to both questions.
If magic requires study, where do you go to learn about it? How do people fund their training? Is there an apprenticeship system, or are there wizard schools, or is it one-on-one tutoring/mentoring? Is an untrained wizard dangerous, or just an ordinary person?
Informal apprenticeship system, as you're learning an actual, individual craft. "Magic" actually comes after what we'd consider mastery, and is a life-long study.
Do wizards have a special language that is used for magic? If so, where do they learn it? Is it safe to chat in this language, or is everything said in it automatically a spell? If so, how can it safely be taught to new students?
Nope. There's actually only one language world-wide, although isolated cultures do sort of develop dialects. But this a world that didn't have a Tower of Babel incident, and so there isn't the tendency toward mutual unintelligibility. There's probably some technical terms that aren't part of the general vocabulary, but not too many.
Is magic considered a science, or are scientists and wizards enemies or rivals? Are magic and science compatible? To what degree does the presence of magic, magical objects, and wizards replace technology (for example, a chest that is enchanted to keep its contents cold could replace the refrigerator)? Duplicate technology? Supplement technology?
There's no line between the two. Technology (which is all hand-made and mostly what we'd consider pre-industrial revolution) is made with "magic" as often as not.
Note: this is not originally how I thought of magic, in the early version of things; I'd thought of it as an additional line of study (like chemistry or physics), and that it would meld oddly with machine-produced items.
Are wizards above or below the law — I.e., do they have full rights as citizens, no rights, or can they do as they like without regard to anyone else’s rights?
Exactly the same as any other citizen.
Is the relative power of a country or ruler usually measured by the size of the army, the number and ability of his wizards, or the amount of money at his disposal?
By the skill of its craftsmen and its ability to support itself. There are, for the most part, no real standing armies--just very low-key militias if anything.
Are certain spells (as opposed to magic generally) illegal? Why — because of the effect of the spell, or because of the ingredients or procedures needed to cast it, or what? If so, how would a criminal magician be detected? Apprehended? Punished? Is catching and punishing illegal magicians the responsibility of the magician’s guild, or do the ordinary courts have to handle it?
No. As I've said earlier, there are no spells. If a craftsman made something knowing that it would injury the person using it, that would be treated as any other instance of one party injuring another--like chucking a rock or setting something on fire. There's only one set of courts for everyone.