Welcome fellow early retiree! You've found a very rewarding hobby, and one that absolutely requires lots and lots of patience.
For your questions, yes, you can use your stove to heat or even just begin heating your oils. Using a water bath/double boiler/bain marie setup can help get them heated to the correct temps without accidentally scorching your oils.
I'm inclined to say the one shop keeper was correct, hot and cold process are pretty much the same thing, the only difference is that with hot process you apply external heat to hurry along saponification. Cold process you let it provide its own heat mostly, and it saponifies at a slower rate.
As far as relative difficulty levels, I'd say that hot process is actually a bit more difficult than cold process. You have to keep an eye on your soap, making sure it doesn't volcano or get too dry or too hot (soap can scorch- burnt soap does not smell nice) with HP. With CP, you don't have quite so many worries about temperature effects (unless you use a fragrance or additions that cause it to heat up beyond what it normally would). You also, as Toxikon noted, are able to do a lot more design-wise with CP.
Yes, how often you stir HP soap can make a difference. The more you stir, the more water it loses during cooking, which will make it more difficult to get into a mold.
Zap testing, done correctly, is no worse than putting your tongue across the terminals of a 9v battery. IrishLass also wrote out instructions how to do it here-
http://www.soapmakingforum.com/showthread.php?t=63199
I deliberately zap tested a soap I knew still had unreacted lye in it, just to see what it felt like. Seriously, it's like a quick electrical shock. Surprising, and if you've done it correctly, not even painful. Unmistakable, though.
Chemical pH testing will NOT tell you if you still have unreacted lye in your soap. The zap test does, reliably and safely.
