Hi Mark
When you put 2 caps in series you halve the capacitance, so it is 50uF. They are back to back to form a non-polar electrolytic (this is how they construct non-polar electrolytic caps). But they still suffer leakage current (but probably very small in value). You want a large capacitance here because you really only want to servo off the DC component of the output and this circuit is what is usually applied to do this function. It is an integrator so you want the pole at the origin or as close to that as you can realistically get it. Leakage in an integrator is not ideal. You want as perfect a cap as you can achieve.
Your 0.1uF are too small for effective low frequency response in this circuit application.
2N4401 are commonplace digital transistors. The 2N5088 would be a better low noise choice if that was what was originally specified.