Cheers! Good deal on spotter training. After the webinar, it still might be a good idea to look at some of those other resources, especially the YouTube playlist. Diversify the portfolio, or... something.
As for your questions: A clear slot is not the same as a hail core, though the RFD (which forms the clear slot) can sometimes steal some hailstones and slingshot them through the area of the horseshoe and clear slot. If you find yourself near a clear slot/horseshoe, be vigilant. But the bigtime hail barrages don't fall there naturally. You'll learn about the precipitation core, FFD, and all the action that happens on the forward flank side of the storm in your spotter webinar.
As for visually identifying a clear slot vs a hail shaft, the clear slot looks like the photo in my previous response (photo was taken from the South/Southeast). The updraft base won't form a clear slot until the RFD comes barging in, though. Like Skip said in his video, the clear air may not always be visible, but the horseshoe usually is. I can only speak from my experiences, so I won't say that it will never look differently. But if you're a visual cues person (and you should be if you're near a supercell), the horseshoe is a good sign that a RFD cut is in progress. Hail will usually occur with the heaviest precipitation, and look like lighter/whiter streaks if you are able to see it sufficiently lit from your vantage point. Here's another photo I took last year:
This was taken from the West/Southwest (the 'back' of the storm). I got a late start and had to literally chase after this one as it moved away from me and to the left. See the hail shaft near the left edge of the picture? That thing dropped icy baseballs near Sterling, CO. I was never in a position to see the updraft base, so I can't tell you if it had a RFD cut/clear slot or not. It did not produce any tornadoes.
Does that help? Your spotter class will help you more. There are plenty of other threads here too, if you do some searchin'.