The parallel resistor is a biasing feedback resistor to help the crystal circuit to oscillate when used with logic gates or inverters. It provides linear operation. The series resistor limits crystal dissipation which is not good for minimizing long term frequency drift and aging.
R1 may lower the Q of the oscillator.
The rise time I think it's the rise time of the generated wave form ,whose frequency determined by the crystal. So here's something with EMC and EMI, short rise time introduce more harmonics and frequency expansion.