I agree there is no reason why 1.6E-19 is the fundamental charge along with a handful of other numbers such as G, the stregnth of the EM interaction that just are. Whilst its always nice to be able to justify as much as possible I have no problem with a few fundamental constants being what they are, if we don't like them we can always adjust all the others so the look like nicer numbers. Essentially thats all a constant is, a way to link a number of variables. As to why there are no electrons with a higher charge I'm not sure why there would be. Looking at the question a slightly different way and asking why do we have what we know of now. We have a set of bosons required to carry forces (2 of them hypothesized before discovery), a set of hadrons each an individual solution solution of QCD (again a number hypothesized before discovery not sure how many but the omeqa particle is the most famous as it completed the baryons). Leptons seem to have been discovered in a more ad hoc manner mostly because half of them only intereact with the weak interaction. It seems to me that the particles that exist are selected by interaction, to me the bigger question is why do the intereactions have the properties they do. As for time varyiance of the charge of the electron, im still not following to be honest. Im not sure why it should change. Certainly that would effect it being called a constant, although there were those claims about light I suppose. As for underlying principles we seem to have a pretty good understanding of the underlying mechanics of the universe. Although I agree with you that we are a little short on underlying principles. Although in much teh same way as mathematics I suspect physics will always have a number of axioms (hopefully 1 eventually) that we have to accept is the reason. Not that I suspect that that particular day will be coming any time soon.
I am not a fan of String Theory at all. To me it is kind of like not being able to do arithmetic, but trying to explain the lack of that ability through calculous. There are sooooo many apparently fundamental things and forces in the universe that we do not even have a slight grasp of yet that it is a little bit presumptuous to try and explain them all at once. As far as the different dimensions, they are very complicated and eloquent white out. For the most part whenever a mathematical or theoretical dead end was reached or perceived the scientists simply used a new dimension to explain it and continue on, rather than figuring out why they came to a dead end. That is why the number of dimensions in the theory keeps going up. It just doesn't jibe to me.
Indeed, i totally agree with that. Whether thats because im an experamentalist,largely cos my maths sux at that level but hey. I do agree that for something to be real science it must be backed up as an acutal physical reality.