It is parallel fed because the DC plate current does not flow through the inductor. R3 may be replaced by an RF choke if desired. C3 keeps B+ from appearing across the variable capacitor which is generally a no no. If R1 were not present, C3 might not charge up and there would be B+ on the variable capacitor anyway. R1 makes sure that the inductor and the outer plates of the variable capacitor are held at DC ground potential. The tuning capacitor is sometimes known as a split stator but is actually the familiar dual ganged capacitor. The rotor and drive shaft are at both AC and DC ground potential. The capacitor is, in effect, center tapped. This will place the center of the coil at AC ground potential. The effect of this is to cause the AC voltage at one end of the tuned circuit to be 180 degrees out of phase with the AC voltage at the other end. Since the plate voltage is 180 degrees out of phase with the grid voltage, the voltage fed back to the grid has the proper phase to reinforce and sustain oscillation.
The two halves of the variable capacitor need to be the same size or in a constant ratio to one another. If the oscillator is to be tuned over a narrow range, the capacitor on the plate side may be fixed and the variable capacitor on the grid side would have a fixed capacitor in parallel with it to limit its tuning range. The AC voltage supplied to the grid is considerable. On the positive peak it drives the grid positive and C2 will be charged. When the grid is forced positive it begins to attract electrons to itself and current will flow. The grid acts like the anode of a diode. This current causes the capacitor to charge with the end of the capacitor which is toward the grid being negative. The grid never goes very far positive because the capacitor charges up and holds the charge. A small amount of charge leaks off through R2 but gets replenished on the next positive half cycle. A substantial average DC voltage, as much as -50 volts, is developed at the grid and this voltage makes the oscillator self adjusting. The negative bias lowers the gain of the tube and it will set itself to exactly what is needed to sustain oscillation. When the grid voltage goes negative, in most oscillators this will drive the tube into cutoff. This will cause the plate current to flow in short pulses but the tuned circuit rings like a bell and the waveform at the grid is a very good sine wave. The wave at the plate may not be as good.