Is it normal for ALL the stores to just be completely wiped out of inventory all at once? I was doing quests and all of a sudden, all NPC shops were all sold out... Is that typically what happens?

Yep I believe they get cleared out at that time every day :)

It is good to complete your quests before then if you can. You make more sP that way because you are more likely to find stuff in official restocking shops at wholesale prices. After 2am you are only going to find restocked stuff in user shops so there's a markup.

If you can't finish before then then wait until 5am or so to restart doing them. This gives shops a chance to refill.

Yes, that's normal.

Now, if you're referring to the pirate shop, that isn't normal for the event and there's something weird going on.

Thanks everyone! Good to know! Will keep that in mind for the future!