It's a roleplaying game by John Harper over at Evil Hat Productions. Have a look. Its mechanics are pretty streamlined, and it's especially well-suited for groups that have different people from week to week.
Nope. Just built-in Javascript pseudorandomness.
That, and the one law no one escapes. Not gravity; the other one.
My Exalted group plays BitD when quorums for the Exalted games can't be met; they're my playtesters. I also got some CSS help from callmenick.com and cssfontstack.com. Many of the colors are taken from Ethan Shchoonover's Solarized color scheme, but I tweaked the accent colors a bit.
Blades in the Dark uses a lot fewer dice per roll than Exalted. I'm still experimenting with just how many there should be, and if that number's pretty low, I'd like to make the buttons a little larger because they'll be easier to tap on a phone.
Those are just so that you can remember which roll in the log went with which kind of action. They don't affect the outcome of the rolls at all. If you leave it blank, they'll be numbered.
Not directly. Use a screencast, or...isn't there some Spider ability that lets you seal promises? Try that.
The tall format is intended to sit on one side of a widescreen display while you consult a PDF or something on the rest of the screen. Or you can view it on a portrait-oriented mobile screen.