My second question is how to properly shift from sunset to stars to moon settings properly without creating a jittery timelapse (I use LRTimelapse for editing, btw).
For timelapse sequences at twilight, you will get best results by using a bramping intervalometer ("bramping" = bulb ramping). A bramping intervalometer not only controls the time between exposures, but it also controls the duration of each shutter actuation, to slowly ramp up or down the exposure time to account for anticipated changes in lighting conditions (such as increasing/decreasing sunlight at dawn or dusk).
However, even with a bramping intervalometer, there will be some unavoidable shot-to-shot variability or flicker, even if lighting is constant. The primary reason for this is because the aperture cycles between fully opened and closed (to the desired set point) for each shot. Before the camera takes a photo, its aperture is fully wide-open, regardless of the aperture you have set. This is to get as much light as possible through the lens, in order to help the autofocus and metering system. Once you actually take a shot, the aperture is closed to the desired size, and the shutter is then actuated.
For most modern camera brands, the aperture is electronically controlled. The glaring exception is Nikon F-mount cameras with non-E lenses. This includes pretty much all Nikon bodies older than 10 years, and all more recent Nikon DSLRs with most 3rd party lenses, and any Nikon non-E lens (which is still most of their lenses).
For instance, your Nikon D7500 is capable of controlling an electronic-aperture F-mount lens (Nikon's own electronic aperture lens have an "E" suffix, such as the AF-S Nikkor 28mm f/1.4E ED). But the aperture on your Tokina 11–20mm is actuated by a mechanical spring-loaded linkage to physically open the aperture. The opening-and-closing action of your lens's aperture has a lot more shot-to-shot variability than a EF-S mount version of that same lens mounted on a Canon body.
Not that any of this is fatal to your process; tools like LRTimelapse will do a good job of smoothing out the flicker. But it's good to know why th input sequence still might have some flicker, even when using a smooth bramping intervalometer.