Re: unknown oscillator type
Explaining as simply as I can:
The transistor is connected in a configuration that inverts the signal fed into it. If the base pin goes higher in voltage, the collector voltage will reduce, so the signal is turned upside down.
To make an oscillator you need positive feedback, meaning some of the output signal is fed back to the input in such a way that it reinforces it, causing an instability that changes the output cyclically. Those cyclic signals are the oscillations you want. If the feedback is negative, meaning it cancels rather than reinforces the input, you get a stable amplifier instead of an oscillator.
If you took the feedback straight from the collector of the transistor, because it is inverted, you get negative feedback which is no use at all. This is where the center tapped transformer comes into play. The transformer primary winding is all in the same direction, think of it as a single coil with a tap in the middle. This means that if you take the tap as a reference point and inject a signal at one end, the other end will have the same signal but turned upside down. This is how the oscillator signal gets inverted before going back to the transistor. The transistor inverts, the transformer inverts again so it is now the right polarity to achieve positive feedback.
Hope that helps.
Brian.