I was under the impressions that Comstock could not see any futures and it was the Archangel (older Elizabeth) that gave him his "prophecies."
No, Comstock saw timelines (probabilities) using the Luteces machine and he based his prophecies off of these probabilities. The 'archangel' figure is just propoganda to feed into his own cult of personality. Old Elizabeth cannot create tears for Comstock because Old Elizabeth's ability to create tears was severely removed. The operation that would be incurred on her if Booker didn't succeed would make it extremely painful for her to open tears (this is in a Voxophone). The pain-tear association stops her opening tears and she never destroys the siphon, which presumably draws almost all of her power away. When she meets Booker in 1983, she says it basically took everything she had to bring him there.
EDIT: As for why he didn't see his own downfall, that wasn't a probability until he sabotaged the Luteces' machine.
EDIT: As for the origin of Columbia, he founds it in 1893 if I remember correctly, this is the exact same year that the Luteces figure out how to make a particle float and the same year they can create tears.
EDIT: Ignore that, I need to confirm that this occured before the founding date.
Ok, so:
A City, Suspended
August the 10th, 1890
Location: Financial District
I had trapped the atom in mid-air. Colleagues called my Lutece Field quantum levitation, but in fact, it was nothing of the sort. Magicians levitate -- my atom simply failed to fall. If an atom could be suspended indefinitely, well -- why not an apple? If an apple, why not a city?
So that date is when she manages to make things float. Do we know precisely when she began experimenting with tears?
Whispers Through The Wall
October the 15th, 1893
Location: Grand Central Depot
The Lutece Field entangled my quantum atom with waves of light, allowing for safe measurement. Sound familiar, brother? That's because you were measuring precisely the same atom from a neighboring world. We used the universe as a telegraph. Switching the field on or off became dots and dashes. Dreadfully slow -- but now, you and I could whisper through the wall ...
A Window
October the 15th, 1893
Location: Founder's Books
Brother, what Comstock failed to understand is that our contraption is a window not into prophecy, but probability. But his money means the Lutece Field could become the Lutece Tear - a window between worlds. A window through which you and I might finally be together.
One And The Same
October the 15th, 1893
Location: Salty Oyster Bar
You have been transfused, brother, into a new reality, but your body rejects the cognitive dissonance through confusion and hemorrhage. But we are together, and I will mend you. For what separates us now, but a single chromosome?
The propoganda states that Elizabeth was conceived in seven days during which Comstock was caring to Lady Comstock. Seven days before that is October 8th, the day Elizabeth was taken and when the male Lutece seemingly crossed over, the same date as the ending. These diaries are for him, so he can be 'mended' by female Lutece, so he can get his memory fixed.
EDIT: Actually, perhaps the reason Comstock was absent was because they were trying to prevent the cognitive dissonance from killing the child.
EDIT: Also, I love how the priest echoed the first thing directly said to you in Rapture "Is it someone new" as the splicer asks you when you rise in the bathysphere.