If a high school had given permission for a low pass over a football game, would the controllers also give permission? The school is about 3-4 miles away from the class D airport. Also, would you have to still stay at least 500ft above ground? I'm assuming you would still have to even if the school is allowing lower because that is the law.
First, the high school has no authority over the national airspace system so any 'permission' is meaningless, at least from the aviation point of view. I assume you want to coordinate with the school for timing and so on, but they can't approve or deny your flight, or tell you what altitude to fly at. (I'm ignoring any school disciplinary issues here, e.g. you're a student and the event is during class time.)
Second, the class D controllers probably won't mind provided that you give them some advance notice (call them a week or two in advance) and keep talking to them while you're in the air. Similar flights happen all the time in controlled airspace for photography and other reasons, so unless the stadium is right under final approach it shouldn't be a big deal.
Third, 14 CFR 91.119(b) says that the minimum altitude in this case would be (my emphasis):
Over any congested area of a city, town, or settlement, or over any open air assembly of persons, an altitude of 1,000 feet above the highest obstacle within a horizontal radius of 2,000 feet of the aircraft
(And don't forget that 119(a) requires you be able to make an emergency landing without endangering people on the ground.)
If you want to fly lower than that then you need a waiver from your local FSDO, but it's entirely at their discretion so you would need to convince them that you have a good, safe plan.
Finally, it's worth saying that there are a bunch of safety issues associated with doing things like this so if you do go ahead make sure you have a good plan and you stick to it. In particular, decide your minimum altitude and airspeed in advance and don't go below them under any circumstances.
See the answers here. With that in mind, you can get waivers to get past these kinds of laws although that is up to the FAA NOT the high school's permission and frankly their permission means little if anything. The FAA's jurisdiction begins at 500ft in almost all areas and may be to the surface near an airport. While this is constantly up for debate in the courts, the main ruling stems from precedent set in 1946 during this case. Ron's comments are on point; if you can provide your location we may be able to offer assistance on who specifically to call. You can find a list of FSDO phone numbers here.