Whilst you can use a forward converter for charging a capacitor, it is designed to provide a fixed regulated output voltage. This means the switching duty and possibly frequency must change as the output cap charges. The output cap on forward converters is there purely for smoothing. Although I am not overly experienced with forward converters, the turns ratio determines the output voltage. You would either have to implement clever PWM techniques to control the output voltage, or limit the current.. or.. treat the forward converter as a fixed voltage source, and charge the cap via a resistor (which will waste 50% of the energy you use to charge the cap).
your questions.
1) Whilst I'm sure any converter can be used to charge a capacitor, by far the most efficient will be the flyback/boost. The flyback is simply an isolated boost, and is much more suited to large Vin/Vout differences - such as 12V to 300V, or 315V to 5V. It does not necessarily have to be resonant, I mentioned that because the self-oscillating flybacks are, by their nature, quasi resonant. And whilst flybacks are very often used to create a regulated voltage for <90W (generally) they are quite noisy, because you're building up a magnetic field in the transformer on the primary 'on' time, and letting it collapse in the off time.
This makes them less suited to higher power DC-DC, but ideal for capacitor charging, where you dont' need a regulated output - the output capacitor determines the output voltage. The more 'packets' of energy you pump into the cap, the higher its voltage goes, until something gives (either the cap rated, the output diode, or the primary switch which will experience a spike of Vout/turns ratio). You don't have to worry about voltage regulation, control loops or any of that jazz, all you have to do is switch the primary with an on-time that isn't long enough to saturate the core (= sudden increase in current draw, heat, efficiency takes a dive). Then once its turned off, wait for the current in the secondary to stop flowing, then repeat.
2. I cannot same I am an expert in push-pull converters, but often the output inductor is there as a filter, along with the output caps. DC-AC covnerters (as in 12V DC to 220V AC) produce a 50/60Hz sine, or a pseudo sinewave output, which is done via PWM. In order to attenuate or filter out the PWM switching frequency, to leave a relatively pure sine wave, it requires a good filter on the output so switching noise isn't injected into whatever its powering. I agree that there probably should be an output inductor, and many automotive inverters are made pretty cheaply so it was probably just trying to cut costs. Or perhaps it is some form of resonant converter that produces a rather clean output that doesn't require much filtering (unlikely, unless its very lower power).
3. As for efficiency of push-pull vs flyback, as always - it depends. Again, I am no expert and I'm sure someone can explain much better.
Flybacks can be very efficient, especially at lower power because one can simply leave a longer time between switching the primary on, or switch it for a shorter time to give a lower peak current in the inductor/flyback transformer. As you go up in power, because the flyback must *store* energy in the transformers core, the size of the transformer must increase in size to the point where you end up with a rather large transformer, that has to switch at very high frequency just to transfer the power. Push-Pull and forward converters transfer energy *through* the transformer - current flows in both the primary and the secondary at the same time, so whilst the transformer size does increase with power, it does not have to be 'massive' since its not actually storing energy - its a true transformer rather than two magnetically coupled inductors.
Although of course you're after a way of saving some time by using an off-the shelf converter, and modifying it, for high voltage capacitor charging from low voltage, I don't think anything really beats a flyback. I have seen other things like a 'royal' converter (
https://en.wikipedia.org/wiki/Royer_oscillator ) used in DIY strobe circuits, but I cannot comment on their efficiency. They are ideal for driving CCFL tubes and produce relatively pure (read, low noise) AC high voltage, but given the fact an uncharged capacitor presents essentially a short circuit, I am unsure how these converters cope.
That 'flybacks for dummies' article is ideal. Explains everything one needs to know, and the circuit he provides - whilst its for regulated DC output for nixie tubes, can be adapted to charge a capacitor fairly easily, although at low power.
Again: I keep going on about flybacks and boosts rather than other topologies - but I do not have much experience of other converters, so hopefully someone will chime in and either correct me, or provide other possible converters for your task. Safe to say though, every xenon flash/strobe I have seen that runs off low voltage uses a flyback. Perhaps the very high power ones (used for ruby lasers, or light pumped lasers in general) use a different type - I'll google.