C1 can of course be charged from a transformer with a bridge rectifier or by two diodes from a transformer with a centre tap. The purpose of D2 is to make sure that C1 is not charged through R1. Particularly at lower AC voltages this is very important because otherwise the tube looses its idle current between dots and dashes with faster rise and fall times on the CW parts as a consequence. Do not add large tuning capacitors on the grid. The capacitance of the tube itself should be most of the capacitance of the resonance circuit.
Additional capacitance has to be balanced by lowered inductance which makes the bandwidth smaller.
A large bandwidth is good for thermal stability and uncritical operation in general. C3 represents the coupling of RF to the grid circuit. The coupling should be tuned for power match at maximum drive power when full current flows through the control grid. For details tuning the grid circuit R3 is a resistor that prevents the Q of the grid resonant circuit from going very high when the circuit is not loaded by current in the grid. This resistor helps to make the amplifier saturate softly, which is essential in avoiding keying clicks and splatter.