Camping stoves are generally not safe for indoor use. They can produce fumes or carbon monoxide that would be fine outdoors, but dangerous indoors. Check the warning labels before buying anything to use inside.
As for the actual cooking, I don't think that you'll get the results that you expect.
My experience includes an MSR Whisperlite International backpacking stove (white gas), and Coleman two-burner stoves in both white gas and propane variants. Anecdotally, the backpacking stove has limited control, while the two-burner stoves don't quite have the oomph of a real gas stove.
The Coleman links that I provided indicate that the white gas stove has burners that put out 7,500 and 6,500 BTU, while the propane stove puts out 10,000 btu on both burners. Using the REI-provided time for boiling water, I calculated that the backpacking stove puts out about 4,500 BTU (and other backpacking stoves indicate similar times, regardless of fuel).
By comparison, my consumer-grade natural gas-powered kitchen stove has two burners that put out 15,500 BTU, one that puts out 9,500, and one (the simmer burner) that puts out 5,000. Viking offers normal burners up to 18,000 BTU, and a wok burner of 27,000.
However, white gas stoves aren't okay indoors. They're fine while they're burning, but lighting them is a bit dramatic, and once you shut them off they'll put out half-burned fumes for several minutes.
Similarly, propane camping stoves usually put off too much carbon monoxide to be safe indoors.
You are right that the moisture in the potatoes are what's causing the oil to 'foam'. If you don't dry your potatoes sufficiently they can quite easily cause the oil to 'boil' explosively out of the frier; this is why you never pour water on a deep-fat pan fire.
There are various ways to dry out your chips/straws, but one of the most effective ways to is to lay them out on a tray or plate and put them, uncovered, in the fridge for a couple of hours, making sure there are no strong odours in there first. Not only will this prevent too much foaming, it will result in really crisp chips!
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My parents used a wok way back when to make spring rolls, but it depends on what you're using it for.
A cast iron skillet will work for a lot of things, but you don't really get a deep-fry from it. It is great for quickly frying up chicken parts to finish in the oven or frying up cutlets/katsu/schnitzel.
A deep sauce pan or dutch oven works well if you are actually trying to deep-fry. You can put 2-4 inches of oil in it and still only be a third of the way up the vessel. This will allow you to submerge the items you are frying, and still not have the oil close to the top.
As for materials, you can go two ways. A thinner material like aluminum or stainless will respond quickly to the heat you put on it. This works both ways of course, since it means the oil will cool down more quickly if the heat gets too low. Cast Iron is good in this regard (enameled or bare) because it retains the heat. When you add items, it cools the oil, so to maintain the proper temperature and keep food from absorbing more of the grease, cast iron should work better in this regard. Using a gas stove may make this less of an issue though.
As for spatter, you are going to get it regardless. The spatter comes from moisture in the food being violently repelled by the oil. It sinks into the hot oil, boils into steam, and then makes a mess of your stove. A little spatter is to be expected; just make sure your food is as dry as possible before placing it in the oil. Spatter-screens can also help.
EDIT: I found a link that talks about deep frying. Most pertinent to your question is to use a deep-sided pan. This keeps the oil from spilling over when you add your fryables, and also helps to minimize splatter. It will be there, but more will be 'caught' by the pan.
Six Steps for Deep Frying Without a Deep Fat Fryer