....usually, a crystal oscillator has a quite high voltage developing
across the crystal AND the varicap which is in parallel with it. this
AC voltage adds and substracts from the DC control voltage, causing the
instantaneous voltage to change and thus vary the capacitance. the net
result is a damping effect of the oscillations' amplitude.
when you have two diodes in series the AC is causing the voltage to
increase on one diode and decrease on the other. being in series, they
compnesate each other in some measure thus reducing the effect.the
additional cap you mention is more of a DC blocking capacitor, more
than anything else.
As for frequency measurement, the only real way is a counter. lacking
one, zer boat the oscillator on you radio, change the tuning voltage to
the other extreme and guesstimate the pitch of the beat note. nothing
much else you can do, except, may be, see if it works OK when
modulated.
Alex 4Z5KS