1. The transistor has three terminals. The emitter is common to the input circuit and the output circuit. The base is where the input is, so the only terminal left is the collector where the output circuit is. It is more popular at low frequencies because it provides current gain. That is a small base current controls a much larger collector current. 40 dB of current gain is quite common from garden variety transistors.
2. It is called a current controlled device because the output current, Ic, is controlled by the input current Ib. The constant of proportionality is called beta(greek letter), or hfe, or hFE. What is the difference?
Beta is the DC current gain at some operating point.
hfe is the small signal gain when the transistor is biased in it's linear region.
hFE is the large signal gain when the transistor's input takes it from saturation to cutoff and back.
3. A VFO creates a high frequency signal. A counter is used to divide the high frequency down to a lower frequency. That lower frequency is compared to a reference frequency, and the VFO frequency is adjusted up or down as a result of the comparison. That's it in a nutshell. The VFO frequency is a multiple of the reference frequency.