About using a crystal as notch filter
Crystals have an extremely high quality factor, making them only suitable for very narrow bandpass / bandreject filters.

The quality factor is the ratio Q = Centre frequency / Bandwidth. 

For a crystal Q can easily be 100000 so for a 40 kHz crystal that means 0.4 Hz ! Is that what you want ?

1) Crystals aren't designed for parallel or series resonance, they have both ! It depends on how you use them what will be the dominant mode of operation.

2) that depends on the crystal, I was working with a 25 MHz crystal recently and there the frequency difference was less than 1 kHz. Typically series and parallel resonance frequencies are very close together.

3) No, once the signal is generated you cannot "pull" it to a different frequency. The only way to slightly change a crystal's resonance frequency is to add capacitance in parallel with it. But that way you can change the frequency only very slightly. Like +/- 10 kHz for a 25 MHz crystal.

4) If you google "crystal notch filter" and select to see images only you will see lots of examples. Note that they're almost all for frequencies in the MHz range !