Diode and capacitor at the Wien Bridge Oscillator
1) The increase in output voltage necessary to forward bias the two diodes has a larger effect on the output amplitude than the small reduction in gain caused by taking the jfet's gate just 0.7V more negative.

2) you are correct. The negative side of C3 is taken negative (with respect to ground) on the negative swings of the output. This is necessary because the JFET's gate must be taken negative (with respect to the source) to increase the source-drain resistance of the JFET and reduce the gain. So the larger the output amplitude gets, the more negative the gate goes and the smaller the gain is.