It sounds to me like the issue may be that you're crowding the pan.
Basically, to get everything nice and brown and crispy, you need enough space for all of the steam to escape. That picture you showed has potatoes stacked on top of each other -- that means as the bottom items cook, they're going to end up steaming the items above them.
At a diner, they have a large griddle to work with -- they can really spread things out. You're not typically that lucky in a regular kitchen, as you don't have as much space, and you have a lip on the pans that'll hold the steam in.
So, either work in smaller batches, or consider recipes that use an oven -- using sheet pans instead of a pan on the stove solves much of the problem.
One other trick is that most diners don't start from raw potatoes -- maybe with hash browns, but not for home fries, you're not going to get the nice soft interior in a reasonable amount of time unless you start with a potato that's already been baked or boiled. (If you're doing things in the oven, you might be able to, but not in a pan)
Just for reference ... I have a 14" cast iron skillet that I use for home fries ... and it's about the right size for cooking a single large potato, which might be two servings, maybe three for kids. (I tend to cook carb-heavy meals).
update : I probably should've stated this directly -- you want the chunks of potato to form a single layer in the pan, with space in between them.
I feel the same as you Anderson. I found that too and you just made me to do some research, which I found they have different smoke points.
Unrefined sunflower oil 225°F 107°C
Unrefined peanut oil 320°F 160°C
see the link: http://www.cookingforengineers.com/article/50/Smoke-Points-of-Various-Fats
Also, one of the reasons food stick to the pan is the evenness of the temperature of the pan. If you use a thicker pan or copper pan, the heat will be distributed on the pan more evenly and food will stick less. The higher smoke point of oil makes me to believe the oil helps to distribute heat more evenly.
Best Answer
The oil is bubbling very simply because of the water inside the object (eg: potato) that is rapidly vaporized when come into contact with the very hot oil.
Incidently this is a very good thing as done right, all the water coming out of the object keeps it from taking on too much oil, which would cause you to have over-greasy food.
Edit: Also note as @SF commented below, that this can also be a very BAD thing if you put something with too much water into hot oil. Adding this in so nobody burns themselves.