Well, I'll give it a try.
First, there is the big divide between Boxer primers and Berdan primers. Ironically, the Boxer primer, used almost exclusively in the U.S., was invented by an English colonel, Edward M. Boxer, while the Berdan primer, used almost exclusively outside the U.S., was invented by an American, Hiram Berdan.
Boxer primers have the anvil (the part that the priming compound is crushed against by the firing pin) as part of the primer. The case has a single, large flash hole (the hole through which the primer flash reaches the powder charge). A decapping pin can be driven through that hole to remove the primer for reloading, so cases using Boxer primers are often called "reloadable". Berdan primers use an anvil made as part of the case, and (usually) two small offset flash holes. These can be reloaded but only with considerable trouble, so those cases are usually called "non-reloadable". Either type of primer can use any priming compound, so statements like "Berdan primers are corrosive" are not true.
Primer mixtures are what is known as primary explosives or initiators, that is, they are used to initiate other explosives. In other words, they are "primers" for other explosives or rapid burning compounds. They themselves can be detonated by percussion (a blow), or by heat. The priming used in firearms is generally of the former type.
The material used in firearms primers for many years, up to about the middle of the last century, was potassium chlorate. It is a very stable chemical and provides very positive ignition. Its drawback is that when it explodes, the chlorate gives up oxygen, and the residue is potassium chloride. This is like sodium chloride, or common table salt, but is much more active. A rifle barrel in which ammunition using potassium chlorate primers has been fired will accumulate potassium chloride and will rust or "corrode". For that reason, potassium chlorate primers are known as "corrosive primers". Armies generally tended to retain corrosive primers through WWII because of their proven stability in all climates, where the stability of non-corrosive priming compounds had not been proven.
To get around the corrosion problem, primer makers tried (about 1900) a compound called mercury fulminate. This compound was not corrosive, but its explosion left a residue of free mercury. Unfortunately, mercury attacks the copper in brass cartridge cases, and softens the case. For military use, where cartridges were discarded, this presented no problem. But for civilians, who often reload the brass case (the most expensive part of a cartridge), mercuric primers were not acceptable. In addition, mercury fulminate proved to have a fairly short period of stability, so primer makers went back to potassium chlorate.
In the 1920's and 1930's, another compound came into general use, lead styphnate. This seemed the answer, since it was neither corrosive nor mercuric, and the primers and ammunition were labeled "non-corrosive, non-mercuric". But today, with growing concern over lead poisoning, the use of lead styphnate has come under scrutiny.
Even though the amount of lead released by a single primer is insignificant, users of indoor ranges especially may be exposed to a considerable amount of lead from the primers, in addition to the greater quantity of lead from lead bullets. So the industry is moving toward use of primers that are free of any toxic metal; one compound is diazodintrophenol (DDNP), which is still not in universal use due to questions of shelf life and reliability.
But some of the questions you raise have little to do with the priming compound. Primer cups are made with different metals, different thicknesses of those metals, and different hardnesses.
Primers intended for rifle use must be hard to resist the higher internal pressures in rifle chambers, so rifle firing pin springs must be strong enough to properly crush and ignite the primer. Primers for handguns are thinner, so that the lighter hammer blow of handguns can ignite them and because they do not need to resist as high pressures as those use in rifles.
Some primers have a larger charge of priming compound so as to reliably ignite heavier powder charges; these are marketed as "magnum" primers.
Primers made for military use have even harder or thicker cups because some military weapons are prone to "slam fire" from firing pin inertia or the blow of the bolt closing on an automatic or semi-automatic weapon. These primers are available on the market for use in civilian-owned arms of military type.
Conversely, some brands of primers have the reputation of being more sensitive, but I know of no brand that advertises this, and it may be a perception rather than a reality.
Life of primers depends primarily on storage of the primers or the loaded ammunition. Under ideal conditions (cool and dry area) most primers will last indefinitely. A few years ago, I fired .45-70 ammo made in 1880. I had misfires, but most went. WWI and WWII ammo will usually fire, but I had a batch of early Winchester commercial military rounds loaded with mercuric primers that were all dead. It had come from South America, though, so storage conditions may have played a part in the deterioration of the primer compound.
HTH
Jim
