1.
"I take it that for a streetpass to count for the badge, it has to be with somebody with ACNL. (let me know if wrong)"
You're definitely correct, it has to be somebody with ACNL. ^^
2.
"Do the streetpass relays from mcdonalds, home depot etc count? (that's pretty much 99% of the streetpasses to be had it seems in the USA)": From experience, as long as it's someone that has the game (and shows up in your Streetpass/Mii Plaza/Notifications), they should count for your Streetpass badge. However, Spotpass connections seemingly do not count (DLC, special Nintendo characters, etc.). I assume it's because Streetpass only records the people who you pass by who have ACNL, and receive their house/s + character/s. But, what I've noticed, even "Special characters" (besides Reggie) with ACNL as their most recent software, like Kyogoku, won't counts towards the badge because you don't receive their house or character at all.
3.
"Which characters in your town get the Streetpass credits toward the badge?": I feel like this is available for any character. All characters can meet the same Streetpasses, regardless of date received, so I'd certainly assume that any alt character can get the badge too.
"Do all the characters get credit for each streetpass? Is it only the mayor?": Even from my other answers.. I really wish someone could help out on this.
I have no idea if my second character would achieve the Bronze badge same time I do. However, I'd assume (from my experience) that if my Mayor meets some HHA Showcase characters, and then my second character does so later, both of them would receive the same amount of Streetpasses for that day.
4.
"Is it only the character whose home is displayed in the HHA showcase that gets credit towards the badge, or is it only the character who first visits HHA Showcase when new Streetpasses have occurred?": The default is your mayor's house that is displayed in the HHA Showcase. But even then, all characters can receive people's Streetpasses, regardless of whose house was received. As for who visits first, I don't think it matters too much considering I personally had two characters meet the same Streetpass people; I logged in as my mayor in July and met about 4 people from a mall I visited the same day I went there. Subsequently, I logged in as my alt/second character in October and met the same 4 people from the mall I went to in July (hadn't logged in in a while =P). I think there's no difference whether one character visits first or not; they both count equally. I'm pretty sure that if there were two people sharing a cartridge, the default wouldn't limit badges to only the mayor. I think even Streetpasses are considered, regardless of how many alt characters you have ^^! I mean, why would they consider fish, bug, or HHA badges, if they don't count Streetpass badges for alt characters, right? I believe the system data itself counts for any character as long as you log in/meet them.
I wonder if this helped at all (maybe common sense.. lol), but good luck. I'll let you know if my alt receives the badge as soon as my mayor does, though.