a. Depends on what type of plane (and plane configuration) you're on. If it's an AA plane where the next class up from economy is called Business (whether it's because it's a two-class int'l or a three-class domestic or int'l), the mileage upgrade code is C. If it's an AA plane where the next class up from economy is called First, the mileage upgrade code is A. (Note: Knowing the plane type alone isn't always sufficient, because on a few routes AA takes a two-class plane and sells it as one-class or takes a three-class plane and sells it as two-class, with AAdvantage elite members given free prioirity access to the "better" seats in a combined class.)

b. That would probably vary with each partner. I suggest you search on "partner fare code" or something like that in the AA-specific forum to see if you can find an existing post that describes that, otherwise ask there, mentioning which specific partners (AA has dozens!) and classes you're interested in. Also, be aware that it can be tricky with partners, as partners may only have access to a subset of the award seats, but I'm not sure if there's a separate code given to reflect that in all cases. Finally, AFAIK AA can only book awards in classes is "knows about": Specifically, AA doesn't have a "premium economy" fare award, so generally can't book an award into BA's World Traveler Plus "premium economy" class.