Yes, HP soap still has to cure. Some people use more water for HP since some will evaporate off during the cook. You can try setting the water to 35% and see what you think.
I don't cover my HP on the stove for most of the process, because I do it at higher temp with constant stick-blending until it expands, at which time I whisk it down and put some plastic wrap or a clear glass lid over the top. You have to watch carefully to ensure that you can whisk down any further expansions (aka volcanoes). You can read more about HTHP, but for a first time soap-maker, low temp HP or CP is probably safest.
Your pot will still be safe for cooking food as long as it is stainless steel and you wash it well. NO aluminum or non-stick coatings can be used for making soap.
If HP feels too intimidating for you, then use your stove or microwave to melt the oils. Let the oils and lye water cool down to at least 120F (lower if you want), then stick blend to trace and pour into the molds. If it is a 100% CO recipe, CP, and in a loaf mold, you will want to unmold and cut as soon as it is somewhat firm, usually no more than 8 hours. If it is HP 100% CO in a loaf mold, you probably want to cut it at about 2-4 hours max. CO hardens up fast when it is the only oil used!!