I'll answer some of these.
"Just played my first session tonight. I was stoked, and I still am about continuing the campaign. Love the rule system."
Welcome aboard! It's a fun ride.
"It seems to be that Armor Check Penalty applies to any ability that is modified by Strength, Dexterity, or Constitution, and no other abilities? Did I interpret that wrong? At which point an armored mage seems like a most appropriate scenario, if anti-thematic. "
From the book: ACP, A penalty applied to the wearer’s physical
skill checks. So yes, I agree with that part of your assessment. On the send part though, ACP is applied to all classes evenly. A mage suffers it the same as an assassin, burglar, soldier... some classes (soldier for one) get perks that mitigate it as they level and every one else can take the armor feat chain to get relief.
"Is there anything preventing a player being able to cast cure spells more or less indefinitely outside of combat?"
Well yes, but you have to read between the lines a bit. Count the downtime as a scene and you limit their points there.
"A mage seems to be able to case cure spells pretty much at a whim - while the priest, typically a character able to heal, relies upon mend checks (which are limited to twice a day outside of combat) and only if they have "life" as an alignment path is there any room for actually casting heal spells. Is this a purposeful bent, are there going to be more diving casting options in the upcoming magic book? Or arcane casters going to be better healers?"
This is a common 'baggage-carryover' from D&D. Very common. FC priests are not stereotyped into healing. They have a wide
range of things to draw from for build, but are fairly siloed in that build. However they are freaking awesome in that silo. My wife's fire/life priest was hellish on mobs. Summon fire elemental every combat with no roll? Yes please.
That spellcheck roll is one of the prices a mage pays for their flexibility, a priest just makes it so. There are campaign qualities that really make this distinction important.
TL;DR version: Mage is flexible but more fraught with dice-errors. Priest is broad definition but narrow focus with reliable and potent effects.
"Does Damage Reduction or Damage Resistance stack unless it says otherwise? Does armor piercing have any effect against damage resistance?"
Yes and yes, if memory serves. Rules monkeys will have to correct me, running short on time.
"Under what conditions does a character with a Flight Speed need to make a Maneuver check?"
Think of it as making a ride/drive/pilot/check; Only when you are doing something fancy/risky IMHO.
"For the Drake, is "quadruped" anything other than descriptive? Is there anything keeping a drake from using a zweihander with the Drake upgrade?"
The art points to Drakes as Quadruped = 2x wings + 2x rear legs, the D&D wyvern template. This. Drives. Me. Nuts. so we went with a quad = 4 on the floor setup with the fronts being manipulators but poorly suited for folk constructs and thus "Beast" designation.
By the rules anything with the Beast upgrade can be used by a Beast character... so if you tack that on to a greatsword, go for it.