It appears that the right side of L4 is for the IF oscillator tuning
and the left side picks up the signal from the air.
No, L4's purpose is strictly as an antenna, tuned to the received radio frequency signal. It has a link winding to impedance-match a transistor's low input impedance at its base.
C29 couples the antennas' low-impedance RF winding to the transistor base. C29 also serves another purpose: it causes Q7 to operate as a grounded-base oscillator as the higher-frequency local oscillator.
The dual-purpose autodyne mixer (RF amplifier plus local oscillator) complicates capacitor selection. The AM broadcast band is wide:
- Oscillator frequency must track linearly above RF frequency by 455 kHz. over the whole span of the AM band.
- Oscillator must operate as grounded base (grounded by C29), even at its lowest frequency where C29's impedance is higher.
The choice of C28, C30 are also subject to these same constraints. Tracking is sometimes complicated by the mechanical construction of the variable tuning capacitor. Practically all multi-section tuning capacitors turn plates of the RF-tuning section along with plates of local-oscillator tuning section on the same shaft.
In some variables, plate shape of the RF-tuning section differs from plate shape of local-oscillator-tuning section, to aid tracking. In other variables, plate shape for both sections is identical: tracking is accomplished by choice of fixed coupling capacitors - an approximation to proper tracking. The choice of C28 and C30 would involve tracking.
Any designer ensures that Vcc does not vary at any frequency of interest, be it audio, RF, or local oscillator: you can assume it is at ground potential as far as AC signals are concerned. So one end of C28 is essentially grounded.
Why did they choose Vcc instead of GND? Perhaps a board layout issue: Vcc was more convenient. Or perhaps impedances of the Vcc trace (or GND trace) favoured stable operation...sometimes these circuits also oscillate at far higher frequency.