CB, I hope you don't mind that I posted the answers here instead of in private message. These answers were too long for the PM system and Scott and DT might find some of these answers useful.
1. How many luck points does Lizt (neutral Thief) start play with? I see that she rolls 1d3 to determine how much of a luck bonus to add and that she regenerates 1 pt of luck each day, but I don't see how many points she starts with. Ditto for the warrior and Elf.
Your Luck ability score is a pool that can be spent to give a character one time bonuses to a roll (like action points) on a one for one basis for most characters. Lizt starts with 13 (her Luck ability score) and, as a thief, gains 1d3 to a roll for each luck point burnt. Since Alois' score is 9 he has 9, and Gratien 7. Burning luck drops your Luck ability one point for each point spent. This is permanent except for, as you noted, a thief (and halfling) regains their level in luck each night. At times I will award characters a point to their luck score for things like playing to alignment so Luck will fluctuate.
2. What are action dice and how are they used?
Action dice are DCC's version of the action economy of games like D&D. Each round a character can move its normal speed and take an action for each of its action die. All characters can use their action die to make another move (essentially double move action). Each class lists what that class can use its action dice for specifically. For example, warriors can only make attacks; thieves use action dice for attacks and thief skill checks.
3. I gave Lizt studded leather armor. How much does studded leather cost, and should I expense that cost from her starting gold?
Studded leather costs 45 gold. I'll let Lizt keep that for free and leave it to you to determine how she came into possession of the armor. As an aside the -2 check penalty applies to skills that require agility and spell checks.
4. Lizt's character sheet says "Lucky Sign: Righteous heart (turn unholy checks) 1." What is "righteous heart" and how do I use that? It sounds cleric-y. Also, Alois's character sheet says "Lucky Sign: Charmed house (Armor Class) 0." No clue what that is or how it works.
Lucky sign is based off of your initial luck modifier and a roll off of a birth table. Most of the time the luck modifier isn't high or low enough to actually cause an effect. Alois has a luck modifier of 0 which is added to his armor class for no benefit. You can ignore it. Lizt has a +1 modifier but rolled something she will likely never use and so you can ignore it as well.
5. How do criticals work for a warrior? Alois's warrior table says Crit Die/Table 1d12/III. Does this mean that if he rolls a natural 19-20 on an attack roll that hits he will add 1d12 damage to his regular damage roll? Not sure what "Table III" means; I don't think I have that info in the packet you sent.
If Alois rolls a natural 19-20 on an attack roll that hits he rolls 1d12 and gets the result of the critical off Table III. You'll notice each class rolls a different die and uses different tables. You're right, I didn't send you those tables. I'm not exactly sure the best way to deal with criticals in pbp DCC but I'll probably narrate the effect myself.
6. What is the ability score modifier progression like in DCC? In other words, what modifier does an ability score of 15 get, etc.?
Ability score modifiers have a flatter progression than in 3e. The modifiers are as follows:
3 (-3), 4-5 (-2), 6-8 (-1), 9-12 (0), 13-15 (+1), 16-17 (+2), 18 (+3)
7. Charm Person lists a manifestation, corruption, and misfire. Are we using these? What does corruption do? I read about corruption in the DCC Magic .pdf, thank you. My question now is whether we have to roll for corruption EVERY TIME we cast! Eeep.
Yes, we are using manifestation, corruption, and misfire. Manifestation isn't really important, though, and is mostly window dressing. The idea is that magic is obvious, variable, and difficult to control. You make a spell check when casting a spell and corruption and misfire only come into play if you roll a natural one. Essentially, you lose control of the magic and it changes you.
8. It seems like a lot of rolling to get Charm Person to succeed. First there's a Will save, then there's the corruption and misfire rolls, and then it looks like there's a chart detailing when the spell fails, when it succeeds, etc. Am I missing something? Or is magic just harder in this setting?
Magic is harder and more dangerous in this setting. Casting Charm Person would follow this process: Gratien would make a spell check to determine if he succeeded in casting the spell. If his result is a 1 he rolls to see what combination of corruption and misfire results. If his result is a 2-11, nothing happens except that he loses the spell and cannot cast it again until the next day. If his result is higher then he uses the entry on the table to determine effect and rolls for manifestation. His targets roll a Will save (DC equal to the spell check result).
9. Invoke Patron calls for "1 point of spellburn." What is that? Does Gratien take 1 pt damage if he casts this spell? Never mind, found the answer.
For Scott & DT's benefit: Spellburn equals ability damage. You can spellburn to gain a +1 to a spell check for each ability point burnt in this way (except if the spellburn is a component of the spell as in the Invoke Patron spell).
10. Would a PC normally only cast Patron Bond once, ever? Not really sure why this is on my spell list or why I would want to cast this more than one time.
You could cast it as often as you found a patron to bond with if you wanted. More patrons equal more power. The downside is that patrons don't give up power without getting something in return. Think Elric or Faust or old sword & sorcery pulp novels' wizards.
11. How high do the dice go in this game? Up to 100? I see a few references to 32+. Not sure how far beyond 32 the dice reach. Will affect odds-based decision making!
The dice chain is as follows:
d3 - d4 - d5 - d6 - d7 - d8 - d10 - d12 - d14 - d16 - d20 - d24 - d30.
Modifiers, such as ability modifiers or spellburn or magic items, are added depending on the sort of roll and circumstances.
12. My elf's character sheet says "Lucky Sign: Fortunate date (Missile fire attack rolls) -1." What is this, and how does it work?
This is just plain unlucky. Gratien's luck modifier is -1 and is applied to missile attack rolls.
13. How do attack rolls work? 1d20 + ??? Not sure what to add to a d20 roll when a character wants to attack. I assume, for an attack with a weapon, one adds one's Strength or Agility modifier, plus a luck bonus or a deed roll (if relevant).
Yes. Roll your action die (which may be a lower die than a d20 when you gain multiple actions), add your 'Attack' bonus (or result of deed die for warriors). Melee attacks add Strength bonus, missile attacks add Agility bonus.
DCC is basically simplified 3.5 with added magic complexity for weirdness and old school feel. I hope these answers are helpful. Feel free to ask when anything else comes up.
One last thing: Skills.
There are no skills/proficiencies in DCC. Your characters' professions determine their knowledge base. If something comes up that needs a knowledge check, if it is something your profession can feasibly be explained as knowing then you roll a d20 for the check. If not, roll a d10.