is there a general recommended distance between dog holes in both directions?
Common sense says that the holes should be spaced from the vice in increments that are less than or equal to the maximum opening of the vice, so that you can clamp any sized object without needing shims.
In the crosswise direction, consider how large an object would need to be before you'd feel the need to use two dogs at each end instead of one. The holes in the Veritas Carver's Bench look like they're spaced on a 4" grid, but that's a specialty bench that's meant to hold relatively small workpieces of various shapes and from several directions. If you'll be working mostly on narrow boards, a single row of holes may be all you need. If you'll work on wide panels, a row of holes on each side of the bench might make sense. In other words, it really depends on you and how you'll use the bench. If you're not sure, remember that it's far easier to drill more holes than to undrill them.
it is possible there is some hardware that makes use of two or more holes
It's certainly possible, but a tool that depended on a specific hole spacing would have a very small market since there's no standard spacing. There's not even a standard shape for dog holes -- round is popular these days because it's easy to make round holes, but square bench dogs and holes are very traditional.
At what point would you have too many dog holes?
You have too many holes when you could do all the same work just as easily with fewer holes. You have too many holes when the holes get in the way of your work -- small parts or tools fall through them, you need to be careful about positioning your work so that none of the legs of the chair or table land on a hole, etc.
If you're building a bench and you're asking for advice about dog hole spacing, this may be a case where fewer is more.