"Superfat" and "lye discount" are used interchangeably, and even tho they are not identical they are pretty close. Sap values (how much lye it takes to turn a certain oil into soap) are averages. Different calculators will give you slightly different amounts of lye. That is part of why you need to have some superfat in your recipe, to allow yourself a cushion so you don't end up with too much
lye. No soap is moisturizing, but yes a bit of extra oil in your soap can help with conditioning and make the soap feel less harsh. A superfat or lye discount just means that you are not turning every last molecule of oil into soap, you are turning most of it into soap and leaving a little bit of oil left over. Depending on what oils you use, how your water is, your skin type and your personal preference, over time you will learn how much superfat you like. I recommend starting with around 5%, that gives you enough cushion to be safe and should be fine for smaller batches.
It does not matter at all when you add the oils. You do not need to withhold oils to add after trace, there is no math involved at all, just plug your numbers into the lye calculators of your choice and make soap. LisaM I would suggest just putting in everything you want into the pot in the beginning.
I make a lot of HP, and I do not add superfatting oils after the cook. Some people swear by it, I have found it makes absolutely no difference IME. Oh, "after the cook" means as soon as the soap is done and you turn off the heat source, whether that is a crockpot, oven, or double boiler. I do not recommend letting the soap cool, it hardens pretty fast. I always cook my soap in a crock pot on low, and I would recommend low for a rebatch. You don't want to scorch the soap. Yes, you can add a very small bit of water or milk to a rebatch soap.
mbeachy soap, I agree with all the advice you have been given to start simple. I don't recommend using corn oil in general (it really doesn't bring anything fabulous to the party and can be prone to DOS), and I buy regular ordinary (non-virgin, non-pomace) olive oil at sams club. It makes great soap.
I have bought top quality fragrance oils, including almond (also one of my faves) from brambleberry, nature's garden, majestic mountain sage, wholesalesupplies plus, and aroma haven.
eta: welcome to the addiction!