Link to rules.
Take a look at the equations listed there. That should answer your questions in terms of your odds of finding a deposit as well as how long it will take.
As for your question of having to scan different parts of the grid, I assume that you are talking about one terrain grid (as opposed to a whole planet). If that is the case, then it doesn't matter where in that particular terrain grid (or "city" if you would like) that you scan.