1. We're talking about the regular Murphy's that is advertised to clean wood, right?
2. Do you dilute it according to instructions on the bottle?
3. What do you prefer to use to apply it? (natural/synthetic sponge, rag, etc)
I use a synthetic sponge, I dunk the tack in the bucket, rub it well I don't worry about it getting over wet, then when it's clean wipe it off with a clean towel.
4. Do you have to condition after using it every time?
Yes, I do, once you have stripped it you need to add goodness back into the leather. Sometimes I use a thin layer of Pasier Lederbasalm, as well, or instead.
5. What do you prefer to apply the glycerine with? I've used a synthetic sponge in the past, but I'd love to know if there is something better.
A synthetic sponge, only damp, not wet, rub onto the bar to pick up then soap then rub onto the leather.