The Dreamer/WMG

Bea will meet reincarnations of various historical characters
Considering her uncle is named Hercules Mulligan, and he was an actual person, it can be safe to assume that she will meet other characters reincarnated.

Bea is a Time Lord but doesn't know it.
However, her power is limited only going to the past, specifically the American Revolution. This power also can only be harnessed when she is asleep.

Bea and Alex had a fling, and did some "dancing"
On the third panel of page 4, found here, Alex makes the remark that he ""took his turn with her more than once that evening.""

In 18th - century society, dancing more than once with someone who not your blood relation or your betrothed/spouse was a social taboo. Also, the look on Alex's face gives away that he's remembering something quite fondly...so one could think that the "dancing" comment is a euphemism meaning that they screwed, or something like it.

Alan is going to die at the end of the comic
The coughing, and Word of God states he has tuberculosis....well, what else can there be? Power of Love certainly won't save him.

John and 21st - century Alex are going to have a rad bromance at Columbia.
And hopefully get their own spinoff, preferably called The Most Excellent Adventures of John and Alex.

Beatrice has fairy blood or something which causes her to have these weird dreams
Or maybe a brain tumor.

Milly Weaver is an Eldritch Abomination
Obviously.

Alexander Hamilton becomes Beatrice's handler
According to this interview, Beatrice becomes a spy in New York City and sets up the Culper Spy Ring. Since Hamilton refers her in the first place, he will probably be telling her what to do and what she is supposed to find out; and since the ring is under control of Washington, Washington will probably let his aide-de-camp Hamilton do most of the work concerning the ring. Cue the UST between Beatrice and Alexander, much the Alan's chagrin.

Everyone in The Dreamer is in Purgatory/Limbo
For the 18th century cast, since they've already died (or we know they have), they're trying to pay off their old debts/sins/etc. by appearing in some girl's dream, hoping that maybe she'll set things right for them, and they can finally go to Heaven. The 21st century cast is also in Purgatory/Limbo, paying off their sins as well.

Ben Cato might be a reincarnated Nathan Hale
I've been rereading some of the past chapters and spotted Nathan reading "Cato and Other Works" link And considering it's influence on Nathan link and then Ben's last name just happens to be Cato?

And then Yvette shares Howe's last name. Which I doubt in the world of story telling is just a coincidence.

I'm just trying to figure everyone else out now.

Yvette = Admiral Howe and Liz = Betsy Loring
OK, how's this for wild mass guessing?

The historical timeline is the "real" timeline. During the six months Beatrice Whaley spent in the company of Admiral Howe and Betsy Loring, she became friendly with them.

When Alan Warren rescues her, she subconsciously creates an elaborate alternate reality in which she is a high school student with no memory of her time on the ship. Thus, she can honestly tell the American rebels that she doesn't remember any useful information about Admiral Howe, and not betray him.

In her fantasy world, she creates people who represent elements of her real life. Her two best friends are Yvette (representing Howe and sharing his last name) and Liz (who represents Betsy Loring - Liz and Betsy both being nicknames for Elizabeth).

However, Beatrice loves Alan Warren and thus her subconscious serves up a way for her to use her knowledge of Admiral Howe's plans without revealing them directly. In her fantasy world, she sees a painting of the Battle of Bunker Hill and mistakenly believes it is Alan, not his cousin Joseph, that dies there. Thus she rushes out to "save" him and leads Nathan Hale to witness the invading British army.

I don't yet have a guess for the reason for this, but her subconscious also provides a barrier for her romance with Alan in the form of a high school crush on Ben Cato (who is based on her Uncle Hercules' slave Cato, whom she got to know during the time she spent living with her uncle). I'm guessing she's very fond of her uncle AND that she figured out he was spying on the British. Although she presumably did not rat him out to Admiral Howe, she may be experiencing conflicting loyalties which manifests as teenage angst in her "modern day" world.

Beatrice is a Reality Warper.
It's just that her talents have been lying dormant until adolescence, and right now she can only warp during sleep.

The Dreamerverse and Neon Genesis Evangelion exist in the same universe
Beatrice's dreams are an experiment on Instrumentality, just to see how it would affect on a small-scale, say an individual. Beatrice's father could be an operative for the US branch of NERV, and may have volunteered his daughter to be a test subject. The results of the testing are the dreams she's having, which cause her to question her reality.