An important note is that pH is the -log[H+]. Thus, when the [H+] increases, the pH will actually fall due to the negative sign. That is simply how it is defined, so adding H+ ions by definition cannot make a media more alkaline. To answer your other question, it is not the Mg and Ca ions that are affecting the pH, rather their oxides and their reaction in water is what affects the pH. You use the example of lime, CaO or Ca(OH)2. This reaction takes place when Ca(OH)2 is added to water. Ca(OH)2 -> Ca2+ + 2OH-. The OH- ion is responsible for increasing the pH of the substance, increasing its alkalinity. (More OH- means less H+, less H+ by definition will increase pH.) Also, I wouldn't necessarily agree with your textbook's statement that pH is a measure of the reactivity of the substance. I think you may be not interpreting your textbook correctly. More on reddit.com

The p is shorthand notation for -log_10(moles/ liter H+) The way the math works out, low pH just means lots of H+ ions. More on reddit.com

There are some great explanations in this thread, and I wanted to add a medical example. Base chemical burns on the eye are worse than acid chemical burns because of the different way the chemicals damage the tissue. If you accidentally splash a strong acid in your eye, it damages the tissue by denaturing it (changing its structure, a common example of denaturing is egg whites turning from a clearish liquid to a firmer opaque white when cooked). The damage stops there, the tissue has been denatured but it does not penetrate deeper. In contrast, when a strong base (such as lye or bleach) hits your eye, it causes saponification (converting fats into soap) and penetrates deeply into the tissues. This causes a lot of damage to the fatty acid membranes of your cells, and it keeps seeping down to deeper levels as it damages. In either case, make sure you wear eye protection when you are working with strong chemicals! And if you get anything splashed in your eyes, immediately flush it with water (it can take 15-30 min of rinsing). More on reddit.com

You wouldn't make it more concentrated, you would start with concentrated acetic acid which is 100% and dilute down to an appropriate concentration. Dilution can only increase the pH so much, as you're only adding acid. If you have ever looked at a titration curve, you'll notice that as you add base to acid there isn't much of a change until you get close to the equivalence point where they neutralize one another. Once the base is in excess, it again plateaus, no matter how much base you add. More on reddit.com