1. To what degree does ammo capacity come into play in typical self-defense situations?
A vanishingly small degree. An older FBI study showed a typical defensive shooting scenario ended in 2.4 rounds with a revolver, 2.8 rounds with an auto, as I recall. The data set was, while smaller than the FBI's, of substantial enough size to be valid as it was longer in duration. The findings also agreed very closely. Six shots should get through two separate SD shooting in a day, with one round left over in the wheel gun for the trip home.
2. We are told that most self defense encounters end in “2 or 3 shots” but is this really the case? It would seem that most police shootings involve many more than 2 or 3 shots, and I understand self defense is very different from police work, but aren’t we potentially going up against the same criminals when they try to do harm to us?
You can google the FBI study for results. Another recent, thorough study was done about 2002 or 2003 by the DC metro police. They found their officers employed on average 2.7 or so rounds per "officer involved" shooting. The data sets were all with the time period they had used double stack autos as duty weapons and not from revolver-issue days. The statistics were well presented by various stratifications - including animal threat, one perp/multiple, one officer/multiple, etc. Again, you can google and locate this. There are a number of thorough studies by LE agencies out there that support this; it's not a myth. Just do the homework.
aren’t we potentially going up against the same criminals when they try to do harm to us?
An easy error to make. SD shootings typcically involve home invasions, workplace robberies, and thwarting personal assaults for the most part. Typical criminals don't prey upon known armed victims; they are usually surprised by the armed response. Likewise, they don't "invade" or rob police stations, or tend to try to rape or mug uniformed peace officers. Regular reading of the NRA's "Armed Citizen" column can give you a good feel for the data and details of these scenarios.
The gunfights that police get in are usually with already hardened, armed criminals fleeing arrest. It's a very different scenario. If I were a cop I would probably want a double stack in .40S&W and I would run various scenarios and drills with it at least twice a month or more. There are depraved individuals out there and if my job put me in direct contact with them I would be paranoid about it. There is an interesting web site called "officer down" or something like that. It is a memorial to officers killed in the line of duty, and not directly about guns. But the sight chronicles every duty fatality of an officer they can find, and they provide the details of the fatal encounter, too. A surprising percentage of them are when the officer stopped a wanted felon unknowingly in a traffic stop and was shot. Another surprising number are were officers were killed via vehicular homicide in a similar scenario and not shot. The number of vehicular homicides on officers was very surprising to me.
Police shooting and civilian shootings are radically different in most regards. But this isn't something that's terribly apparent until you realy dig into the data and details.
3. How many rounds/reloads do you carry and why.
Six shots or seven depending upon the gun, because I've read the studies above and understand the odds and scenarios. Sometimes I will stick a speedloader or extra magazine in a pocket, but usually not.
4. Has the reliability of the modern, service size auto made the large revolver obsolete for concealed carry?
A modern "service size" auto is far too large for routine concealed carry, and it seems has actually highlighted the value of a smaller, more concealable gun. As to large revolvers vs. large autos, that's up for debate. The revolver maintains a reliability and safety advantage despite reduced ammo capacity. Some thinking people will always "do the math" and find that advantage a worth-while trade-off. You can not make a rule that suits everyone, as people have different priorities. While modern autos can be terribly reliable, the fact is they are still dependent upon their ammunition shape and integrity for loading. Revolvers are free from this criteria.
Also, I don't know if there's not a presumptive fallacy in your Question 4. It sounds like you are asking if a large auto has made a large revolver obsolete for concealed carry, correct? I would question whether that presumption is even sound - that large revolvers were popular choices for concealed carry. Large revolvers have historically been duty guns carried openly. Small and medium sized revolvers, and small autos, have historically been the most common concealed carry guns from my observations.