edit: Um, Neeners, I regret to differ with you. The quick chemistry answer is this: The fats break down into fatty acids and glycerin. The fatty acids react with the lye (a base) to form soap molecules. But read on for the long answer........
Yes, soap will always be alkaline, even with superfat. The natural alkalinity of soap is determined by the reaction kinetics of the fatty acids and the base (the lye). It's hard to explain it fully without getting into a chemistry course, but here's the best brief explanation I can offer:
Fatty acids are acidic, yes, but they are ~weak~ acids. If you put, say, stearic acid on your skin, it is a weak enough acid that it can't damage your skin. A strong acid is something like hydrochloric acid. If you put hydrochloric acid on your skin, it is a strong enough acid that it will definitely cause a chemical burn. The difference is how "willing" each acid is to break apart and release its hydrogen ion(s) (H+) when mixed in water. A strong acid ionizes almost completely. A weak acid does not ionize as easily -- it will only "give up" some of its hydrogen ions when made into a water solution. The natural pH of a solution of water and a strong acid will be lower (closer to 1) than a weak acid solution for this reason.
There are strong bases and weak bases as well. A weak base is bicarbonate of soda (baking soda). If you put it on your skin, baking soda won't damage your skin. A strong base is the lyes we use to make soap -- sodium hydroxide and potassium hydroxide. If you put either of these on your skin, it will certainly cause a chemical burn. The idea is the same as weak and strong acids, except bases release hydroxide ions (OH-) rather than hydrogen ions. The pH of a solution of water and a strong base will be higher (closer to 14, the max pH possible) than the pH of a water solution of a weak base.
So, if you mix acids and bases together -- what happens?
If you mix chemically equal parts of a strong acid and strong base, the resulting pH may indeed be close to a neutral (7) pH. What a neutral (7) pH means is there are exactly the same number of OH- ions in the water solution as there are H+ ions -- they cancel each other out, in effect. But that's not necessarily true when you mix, say, a strong base with a weak acid.
The pH of such a mixture, even if you carefully measure out equal parts of each chemical so they should precisely cancel each other out, will still not be neutral. The reason for that, as I've explained, is that the weak acid does not easily give up the H+ ions needed to cancel out the OH- ions from the strong base. The weak acid gives up ~some~ H+ ions and thus lowers the pH of the water solution, but it won't give them ALL up. Vice versa is true in a water solution of a weak base and strong acid.
When we make soap, we're combining a weak acid with a strong base just as I've described. The resulting bar of soap is not a boringly static, unchanging block of stuff. Soap is a "colloid", meaning it's a complex structure of solid soap crystals surrounded by a film of water-based liquid. The chemistry going on in this colloid is constantly changing -- it's like a huge party where all kinds of microscopically tiny people are circulating around. Some people "hook up" with each other and some just cruise. Some may hook up, but later unhook, cruise for awhile, and hook up with someone different.
In chemistry terms, all this partying and circulating is called a "dynamic equilibrium". Obviously, many soap particles are created when the fatty acids and the sodium ions "hook up" more or less permanently to form the chemically neutral molecules we call soap. But there are also the chemical loners who circulate in the watery liquid inside the soap structure -- these include some sodium ions (Na+), some fatty acid ions (Ste- and others), and the H+ and OH- ions released by the lye and the fatty acids.
In soap, the pH of this dynamic equilibrium is naturally alkaline, meaning there are more OH- ions from the lye wandering around than there are H+ ions liberated from the fatty acids. This will be true EVEN IF there are exactly as many fatty acid ions in the soap as there are molecules of lye -- or even if there are more fatty acids and fats than lye molecules. It's just the nature of the beast when you're dealing with the dynamic equilibrium between a strong base and a weak acid.
Whew! That's enough for now -- I'm going to let others chime in on your other questions ... gotta get back to work!