Heat stabilizer helps keep your colors stable when heating so they don't discolor. Really handy for light colors like bubblegum, white, clear, chartreuse, hot pink, etc. Add it to cold plastisol prior to heating. Add to remelts when they are getting to be more liquid. You can do without, but it's helpful.
Add softener to liquid plastisol to make your finished baits softer.
Worm oil has a ton of uses, from lubing your injector to bagging your baits. I'm sure a bunch of the guys will chime in here.
As far as remelts, I've found you need to heat in increments and stir. I usually will heat for a minute and then stir. After that I stir every 15 to 30 seconds depending on color and how far along the melting process they are. (Usually it's 1 min, 30 secs, 15 secs, 15 secs, done). If you just heat it without stirring you're more likely to burn or discolor your plastic and more likely to get microbubbles.
I would highly recommend starting out with some fresh plastisol before delving to deeply into remelts, it's just an easier process and will help you become familiar with your equipment. The most important thing is be safe. Melted plastisol is hot, and pyrex cups used for melting it can be even hotter.
Welcome to the forum and the wonderful addiction hobby of making lures!