Hi Kevin - diabetics are in serious trouble if their ketones go high, since, associated with eating high carbs and diabetes, this can signal a dangerous state called ketoacidosis. This doesn't happen in lowcarbers, so don't worry about dark colour.
They say that you should aim to drink half your weight in pounds, in fluid ounces if that makes sense.
So you should be aiming at 140 ounces. Check me on the maths, but I think a gallon is 8 * 16oz, so that would be 128 fluid ounces - so you may need even more water!
You also make ketones from dietary fat as well as body fat, so on induction, eating plenty of fat, you could be making some from that too.
And yes, exercising will burn off some ketones.

Good luck with the journey (and all that water!), take care, Jay