The soap could go through complete gel or not gel at all without CPOP or fridge.
I don't gel my soaps usually I have a recipe that is 40% hard oil and I have both my oils and lye at room temp when I soap (about 25c). The result recipe was very slow moving and did not gel at all naturally even in summer.
With some recipes I've seen people wrapping the mold in plastic wrap then blanket to keep it warm to force full gel. If you have lots of sugar in the recipe (like from juice or milk) it can heat up and cause half-gel, wrapping it can force a full gel.
For CPOP there are different ways doing it. Most people I've seen doing that is have the oven on lowest setting, heat it up, put the soap in, and turn it off. I imagine the temperature actually won't be that high to melt the MP but I'm no expert on this.
I used MP embed both on top and inside the soap. It really only depends on the design you want. The only thing I can say is that you need to watch out for the trace when putting MP on top. Too thin the MP will sink, too thick then it might not stick well. Never really had problem with embed inside, probably because I only do confetti for that so far.