unevb,
i)The Capacitance will keep changing, but the frequency of oscillation will be close to the average capacitance presented through out a full period.  Signal varying capacitance will be a form of distortion which may make the phase noise greater than optimal.
ii) basically the KVco will radically change effecting the loop stability and loop gain.  It will have an effect on the loop bandwidth and gain dropping due to KV will probably make it more stable so stability may not be a concern.  with that said my guess is that phase noise may suffer.  Try to keep the VCO out of this region for the most part unless the system is reciprocal mixing limited and not integrated phase error limited as in a jammerless data system.
iii)  This makes sense since the varactor Q is probably quite a bit lower than the other capacitors in the circuit.  When this lower Q varactor's weighted Q becomes more dominant then the total tank Q decreases thus the amplitude will be lower.

Also worth noting is that most mos devices are not modeled correctly to be suitable as varactors for low noise operation primarily due to gate resistance not being modeled correctly or at all in many cases.  In other words the results will be better in simulation then measured.   Consider trying to unload the burden of tuning a wide frequency range  by the varactor only instead choose a method of switching in capacitance when varactor voltage exceeds a range.    VCO design is a lesser of all evils multi variable optimization.  Where simulation is hard to get accurate and modeling is everything.  

J