Pretty soaps, and I like the coloring ingredients.
Yes, emulsion can happen in a few minutes, for sure. Depends on oils used, temps of oil and lye water, amount of stick-blending, etc.
As long as you completely dissolved your lye in the water (and strained out any undissolved pieces), it is very unlikely that the crystals you are seeing are crystalized lye. They are probably the crystalized soda ash that sometimes happens.
Also, CP soap will always zap for the first 24-72 hours until saponification is complete. Thus, a zap test before then isn't going to be accurate for knowing whether it is actually lye-heavy. You can also search other threads and see that even lye-heavy soaps eventually cure out to be neutral, if you give them enough time. That isn't the same thing as crystalized or undissolved lye, which would be dangerous, but again, is unlikely if you followed normal lye solution procedures.
Sorry, I don't use RA so I can't answer that question. I'm sure someone else can.