It's a roleplaying game by White Wolf in which starting characters are demigods. You can get PDFs of the sourcebooks from DriveThruRPG. They also have novels and manga based on the setting (A Day Dark As Night was free last I checked, and pretty good). There are some good fan-made webcomics too:
Adding a stunt adds dice and autosuccesses to the roll in addition to whatever you have already specified, and reminds you of any related Willpower gains. That way you don't have to actually remember what each level of stunt does.
As an example: You take an action at 4 Dexterity, 3 Melee, with 3 dice added from Charms. The Storyteller awards you a 1-dot stunt for your description. Enter the roll as 10 dice and select the 1-dot stunt; when the roll finishes, you will see that 12 dice have actually been rolled. The stunt added two dice for you.
Not at the moment; it just uses the pseudorandom function that comes with Javascript. (I may bring in true randomness later, though the Pattern Spiders and the Principle of Hierarchy will throw a fit...)
I wrote this to use with the Enduring Lies of the Immaculates campaign, and my fellow players provided a lot of debugging, playtesting, and suggestions. 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 (see what I did there?) but I tweaked the accent colors a bit.
Sure; you just won't use most of the options. In particular, the "Add stunt" option should not be used for earlier editions.
First, the final result is posted concisely, so sorting the result for easy tallying isn't actually necessary. Second, if the dice are left in the order in which they were rolled, you can fairly subtract dice from a roll after the fact if you realize you mistakenly rolled too many. Just ignore as many dice as needed from the right side of the line.
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 (you have to remember to turn off double 10s yourself). If you leave it blank, they'll be numbered.
Not directly. Use a screencast, or play with an Eclipse.
Roll it as "10s not doubled" and add one success after the fact as needed. You'll also have to make extra rolls manually in case of a "Cascading 10s" effect (the one where you roll an extra die for every 10 you get on the initial roll, perhaps recursively). You can use the "cascade" label to remember that all those rolls go together.
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.