WMG / Histeria!

Father Time kidnapped a bunch of children from different historical times and brought them together for the show.
You know how Loud Kiddington's theme song opens with the line "When the world had just begun / There lived a boy named Kiddington"? Apparently, he must hail from the time of cavemen and dinosaurs (never mind that, in real life, cavemen and dinosaurs never coexisted together). This theory must also explain why Charity frequently dresses as a pilgrim - she's actually from colonial times, and she's used to wearing her pilgrim outfit.

The Kid Chorus will go to Acme Looniversity when they're teenagers.
It's shown several times on Histeria! that the Histerians live in the same world as the Looney Tunes characters, who as we know from Tiny Toon Adventures, work as teachers as Acme Looniversity. Right now, the Kid Chorus (including the already-teenaged Toast and Pepper, oddly enough) attends William Howard Taft Big Around the Middle School (as mentioned in the episode "North America"), so obviously when they graduate from there, they'll likely go to Acme Loo.

Froggo and Charity are brother and sister.
They do have blonde hair and calm personalities in common.

Loud, Froggo, and Big Fat Baby are brothers.
Ever wonder why Froggo's last name is never shown, or why he and Big Fat Baby are never referred to by a real name? They're actually Loud's brothers! This fits with the fact that their voice actors are brothers themselves.

Father Time and World's Oldest Woman are brother and sister.
How else do you explain why WOW never romantically pursues him?
  • Alternatively, they dated once, but broke up when she started seeing younger men. Now they're Amicable Exes at best.

Pepper Mills is blind except when it comes to recognizing signatures.
Either that, or she'd have to be really stupid to mistake George Washington for Michael Jackson.
  • It's also possible that she has an extreme case of prosopagnosia, also called face blindness.

The Big Fat Babies are all clones.
This one is supported by a Kids' WB! promo for the show in which they show that the babies are all clones created by Lexcorp.

Lucky Bob thinks Cho-Cho is a man.
That would explain why he keeps addressing her as "sir" despite that she clearly speaks with a feminine voice.

Toast and Pepper are being held back in school.
Ever wondered why Toast and Pepper, the only regular teenage characters on the show, are depicted as being in the same classroom as the rest of the kids? Well, it seems rather obvious that they've flunked school at least once or twice and have had to be held back. Toast mentions in one episode that he had to go through sixth-grade English three times, and the same episode also shows Pepper receiving an F on her book report. Since the both of them are Cloud Cuckoolanders, therefore it doesn't seem surprising that they're stuck in middle school as teenagers.

The Kid Chorus hangs out with the Warner siblings.
Since the Kid Chorus frequently tend to harass the historical adults they visit, it's apparent that they've probably hung out with Yakko, Wakko and Dot, and their behavior rubbed off on them. This theory is further supported by a scene in the Kids' WB! intro sequence in the 1998-99 season, where we can see Toast, Aka, Cho-Cho, and Fetch in the studio water tower with the Warners.

Loud will grow up to be a composer.
Loud's voice actor, Cody Ruegger, has mentioned that he plans to become a composer of film scores. What's to say that his Author Avatar won't pursue the same career?

World's Oldest Woman is Eve.
Explains why she claims to have dated Adam.
  • Alternate theory: She was the demon Lilith, who was Adam's first companion before Eve in some versions.

World's Oldest Woman isn't as old as she claims to be.
She really did know/dated all of those historical figures, but she is really a more realistic age. All of the other characters seem to be time travelers, so why not her? Which leads me to...

World's Oldest Woman was once Charity Bazaar
Her real name was never mentioned. Going by the above theory, Charity will grow up to be WOW. Why Charity? Pepper wouldn't remember historical figures she mistook for modern celebrities with such fondness.

Father Time's first name is Justin.

Charity Bazaar is one of the Ancient Astronauts.
A sketch in the Americana episode reveals that she is an alien in a human suit. It's possible that she and other members of her species came to Earth millions of years ago and influenced some of Earth's history.

Big Fat Baby gets fresh diapers regularly.
I really can't see the other characters being cruel enough to let a baby wallow in his own poop for centuries. It's pretty clear they're time-travellers, so they have a running joke in which they freak out historical figures by telling them the TIME PERIOD they were in when they last changed BFB. For BFB it was likely no more than a few hours ago.