Do they need to stay in your inventory??? Or do you learn them like in the first game, and can get rid of them later?

I believe you need to keep them. I was wondering the same thing. My reason for thinking you need to keep them is that I went into meditation and checked out the alchemy system. Inside you select what you want to make by clicking on the physical recipe, which has the inventory weight and everything listed next to it.

Now the question is could you still make it by adding the right ingredients and just not have the recipe there for the shortcut

Makes sense. They're only 0.1 in weight in either case, but wondered.