How do the voltage of DC voltage sources and capacitors add up in series
I can't quite get my head around how the voltage adds up in a series circuit.


Voltage is always a difference between the potential at two points.

If the difference in potential between point a and point b is +10 V, and the difference between point b and point c is +5 V, then the difference between point a and point c is +15 V. It makes absolutely no difference what kind of components are connected between points a, b, and c.

Just like if a hilltop nearby is 100 feet above where I'm standing, and another larger hilltop is 200 feet above the first hilltop, then I know the second hilltop is 300 feet above me. It doesn't matter what kind of roads or stairways or rope-slides are forming a path between me and either of the hilltops, or between the two hilltops.


  if I were to charge two capacitors separately from a same 1.5 V battery (first charging the first, then removing it, then charging the other). And then combine them in series (like ---| |-----| |---- ). Would the charge across them be 3.0 V (ideally speaking)?


Yes. You don't even have to charge them one after the other; you can charge them at the same time. That's the principle behind a switched capacitor voltage converter circuit.


  If so, what would happen on the plates before and after combining them?


Nothing in particular happens. Each individual capacitor still has the same 1.5 V across it that it had before, so it has the same charge on its plates.