There are additional details that can be added.
Lesser models don't have the E1 or E2 menus, nor Auto FP.
Nikon Menu E1: The Auto FP shutter speeds don't actually set the shutter speed used. Shutter speed is still as automated by metering, or as set manually, possibly still very normal shutter speeds.
However, the mechanical shutter does have a Maximum Sync Speed, typically 1/200 or 1/250 second for Nikon. Because a faster shutter will not be fully open to allow flash to illuminate the entire frame. HSS (Auto FP) is a mode that can bypass that, at great expense to flash power, range, and speed.
Models like your D7200 can actually sync flash at 1/320 in speedlight mode, if the Auto FP 1/320 menu is used, but if the shutter speed is not higher than 1/320 (faster would trigger HSS mode, no longer speedlight mode).
Auto FP does allow that shutter speed to be faster than Maximum Sync Speed (only if such speed is metered as necessary), because Auto FP enables HSS mode (High Speed Sync). The "Auto" means that if the shutter is allowed to go higher than Maximum Shutter Sync speed, when then and only then flash mode changes from speedlight mode to HSS mode (HSS mode is only actually in effect if shutter speed actually exceeds Max sync speed, or exceeds the Auto FP menu notation). Meaning if used with a HSS capable flash. The internal flash cannot do HSS, but it can be controller for a HSS remote flash.
So in Auto FP, the only time HSS is actually in effect and used is when shutter speed is faster than the Auto FP menu notation. That means the capability of flash in brighter areas can vary drastically when auto shutter speed passes Auto FP speed, or returns back down. Which unexpected great variability is an excellent reason to always turn Auto FP OFF unless this HSS feature is actually wanted.
My site describes Auto FP and HSS at https://www.scantips.com/lights/flashbasics2b.html
E1 Flash Sync Speed has another obscure use, if set low, like to 1/60 second, it will not allow a shutter speed with flash any faster (becomes an artificial Maximum Sync Speed). A Slower limit is not likely needed, and the real idea however is to set E1 to to the actual Maximum Sync speed spec of your camera, 1/200 or 1/250 second, depending on Nikon model. The real meaning of this choice is that would also not select, or would disable Auto FP and HSS (HSS has a few downsides). Can always set E1 to Auto FP to enable HSS if and when the situation arises.
Nikon Menu E2: Is Slowest shutter speed allowed if using flash, if modes A or P (however the camera must recognize the flash is present to have effect, meaning compatible communication). Default is 1/60 second, considered slow enough if hand holding. In A or P mode, shutter speed depends on the metered ambient, so due to this E1 limit, flash indoors in A or P mode will surely ALWAYS use this 1/60 second shutter speed (assuming Auto ISO is OFF) - a good reason to consider camera mode M with flash indoors.
A slower E2 menu limit can be chosen, but the only way in A or P modes to make shutter speed faster that 1/60 with flash is to go out into brighter light that will meter faster. Manual mode M has a lot to be said for it when using flash.
The only idea of this slow limit is that flash is normally used in dim places, where the shutter speed might meter very slow, like maybe 1/8 second. The metering of ambient sets the shutter speed (but E2 resets it). But if you are using flash, there is no reason to suffer with 1/8 second, so this 1/60 minimum speed is enforced (in A or P modes). The 1/60 is NOT about metering, it is only about hand holding (about the blur that hand-held ambient could cause). The ambient that meters 1/8 second will then be underexposed at 1/60 second (assuming Auto ISO is OFF), but that's OK since you are using flash instead. It's hard for underexposed ambient to show blur, allowing the fast speedlight to handle those issues. I think essentially all automatic cameras enforce a similar 1/60 second shutter limit with flash.
TTL level can react to Auto ISO, but manual flash cannot. If Auto ISO is Not Off with indoor flash, then the ambient will be raised to normal exposure levels, and then the orange incandescent and the white flash will be mixed White Balance, which is another new problem.
Exceptions to E2: Slow Sync is a sync menu option that ignores this E2 setting of Minimum speed (maximum time). Slow Sync will continue to use whatever slow shutter speed was actually metered or set (and flash becomes fill level for ambient). Rear Curtain sync necessarily also does Slow Sync, wanting to see that blur trail.
Also, camera modes M or S will still use whatever shutter speed was set, ignoring E2 menu.
