Can cement board be used for the curb rather than mortar? If so, how is it to be placed? Any specific installation requirements?
If you are using the traditional preslope and liner method, then you can't use CBU on the curb. If you go with a liquid or membrane waterproofing, then CBU is acceptable on the curb.
Is Hardie Board an acceptable cement board?
Hardi is good in certain applications, and is certainly approved for use in showers. It's not my personal preference for showers, though. If I used CBU in a shower, I'd use Permabase or some equivalent. My primary gripe with Hardi on walls is that it's slightly thinner than 1/2", so it doesn't transition well to drywall.
Do I need a vapor barrier behind the cement board?
If you're going to use a surface-applied waterproofing, such as Kerdi membrane or Redgard, etc., then no, you won't need a vapor barrier behind the CBU. If not, then use 6 mil plastic on the studs.
For the cement board joints, do I need to tape and mud them as well? If so, what is the best thing to use?
You need to tape and mud the joints on any CBU with 2" wide alkali-resistant mesh tape and thinset. The only exception to this that I'm aware of is if you're using Kerdi.
Would Kerdi waterproofing (or similar) provide me with additional protection? Is it necessary?
While not necessary, Kerdi would definitely provide you with a better waterproofing system. It's a little more expensive, but looking at the big picture, it's not that big of an expense. A Kerdi shower will dry out faster, which reduces the chances of mold growth, which in turn makes your shower last longer. There are a number of liquid waterproofing products on the market that work quite well. I've found them to be a bit more time-consuming since you have to allow for drying after each application, but that may not be a concern for you. The advantage with liquids over membranes is that there are no overlaps, so they make tiling easier for a DIY'er.
For the pre-slope, I have seen some posts in regards to using cement board to create the “step” towards the drain; I assume that is NOT recommended?
No, you'll just want to use deck mud.