There are additional details that can be added.
The smaller models do not have the E1 or E2 menus, nor Auto FP.
Nikon Menu E1: Auto FP shutter speeds do not really set the shutter speed used. The shutter speed is still as automated by the measurement, or as set manually, possibly even with very normal shutter speeds.
However, the mechanical shutter has a maximum synchronization speed, usually 1/200 or 1/250 seconds for Nikon. Because a faster shutter will not be fully open to allow the flash to illuminate the entire frame. HSS (Auto FP) is a way that you can avoid it, at a great cost to flash power, range and speed.
Models like your D7200 can synchronize the flash to 1/320 in flash mode, if the Auto FP 1/320 menu is used, but if the shutter speed is not greater than 1/320 (faster it would fire the HSS mode , it will no longer be the speedlight mode).
Auto FP allows the shutter speed to be faster than the maximum sync speed (only if the speed is measured as necessary), because Auto FP enables the HSS (High Speed Sync) mode. "Automatic" means that if the shutter is allowed to go higher than the maximum shutter sync speed, only then will the flash mode change from flash mode to HSS mode (HSS mode will only be effective if the shutter speed exceeds the maximum synchronization speed). , or exceeds the notation of the Auto FP menu). That is, if it is used with a flash compatible with HSS. The internal flash can not do HSS, but it can be a driver for a remote HSS flash.
Therefore, in Auto FP, the only time HSS is actually in effect and used is when the shutter speed is faster than the Auto FP menu notation. That means that the ability of the flash in brighter areas can vary drastically when the automatic shutter speed passes the automatic FP speed, or down again. The great unexpected variability is an excellent reason to turn off automatic FP unless this HSS function is really desired.
My site describes Auto FP and HSS at https://www.scantips.com/lights/flashbasics2b.html
E1 Flash Sync Speed has another dark use, if it is set low, about 1/60 second, it will not allow a faster flash shutter speed (it becomes a maximum artificial sync speed). You probably do not need a slower limit, and yet the real idea is to configure E1 to the actual maximum synchronization speed specification of your camera, 1/200 or 1/250 seconds, depending on the Nikon model. The real meaning of this choice is that neither would it select, or disable Auto FP and HSS (HSS has some disadvantages). You can always configure E1 in Auto FP to enable HSS if and when the situation arises.
Nikon Menu E2: The slower shutter speed is allowed if the flash is used, if the modes A or P (however, the camera must recognize that the flash is present for it to take effect, ie a compatible communication). The default is 1/60 seconds, slow enough if held by hand. In A or P mode, the shutter speed depends on the measured environmentTherefore, due to this E1 limit, indoor flash in A or P mode will ALWAYS use this shutter speed of 1/60 seconds (assuming the automatic ISO is OFF), a good reason to consider camera mode M with flash indoors.
You can choose a slower E2 menu limit, but the only way in A or P modes to make the shutter speed faster than 1/60 with flash is to turn off a brighter light that will measure faster. Manual mode M has a lot to say when using flash.
The only idea of this slow limit is that the flash is normally used in places with low light, where the shutter speed can be very slow, as maybe 1/8 of a second. The ambient temperature measurement sets the shutter speed (but E2 resets it). But if you use flash, there is no reason to suffer 1/8 of a second, so this minimum speed of 1/60 is applied (in A or P modes). The 1/60 is NOT about the measurement, it's just about the grip of the hand (about the blur that the hand's environment could cause). The environment that the 1/8 second meters will then be underexposed to 1/60 of a second (assuming the automatic ISO is OFF), but that's fine since you're using flash instead. It is difficult for the underexposed environment to be blurred, which allows the fast speedlight to handle those problems. I think that essentially all automatic cameras apply a similar shutter limit of 1/60 seconds with flash.
The TTL level can react to automatic ISO, but the manual flash can not. If Auto ISO is not disabled with the internal flash, then the environment will rise to normal exposure levels, and then the orange glow and the white flash will mix with the white balance, which is another new problem.
Exceptions to E2: slow synchronization is an option in the synchronization menu that ignores this E2 configuration of the minimum speed (maximum time). Slow synchronization will continue to use the slow shutter speed that has actually been measured or set (and the flash will become the fill level for the environment). The synchronization of the rear curtain also makes the synchronization slow, wanting to see that blurry path.
In addition, camera modes M or S will continue to use the set shutter speed, ignoring menu E2.