Have you consulted with a hydraulic engineer?
Not really. This falls more into the category of a medium nuisance than a major problem, which is why I'm looking at DIY solutions. As I said, when I have working sump pumps little or no water gets in. Without them, I might get 1/2 to 1 inch of water in a few rooms. This isn't a case of getting a foot of water in the basement every time it rains.
If the street outlet is visible in the gutter, just stick a running hose in the downspout and watch how much water is coming out. Try to compare with how many gpm you're getting direct from the hose.
The downspout drain connects directly to the city sewer. It doesn't go to the street.
Does the downspout empty onto the driveway? Are you sure the water from the downspout is not running back toward the house? Does the middle of the driveway have a fibrous expansion gap filler running down the axis?
See above. I've never seen the drain overflowing or clogged since we've lived here. My neighbor's downspout drain did get clogged.
The driveway had one of those gap fillers. It eventually rotted away but there's dirt and weeds in the crack now. It's definitely not a major source of water. In fact, it seems almost impermeable to water.
It is much more difficult and expensive to stop the flow of water then to redirect the flow of water. This might be the place for the French drain.
You may use your natural water table as a guide to the depth. It is fruitless to go below it.
The water table is way below where the problem occurs. One time I had dug down in the front of the house to fix the cracks outside my workroom. I dug down at least five feet. Didn't see any water.
Unfortunately, the presence of the concrete driveway prevents any major outside remedies like French drains. In retrospect, when we had the driveway replaced 23 years ago we really should have had someone come in and address the water problem prior to laying the new driveway. My mom suggested it but my father was too cheap to pay for it.