Na Na,
Sorry for the delay. Message got lost in holiday activities.
1. For the false lock to occur the FG frequency must be close to the internal clock frequency. It's the internal clock frequency that can vary by +/-30%. So it is possible that the motor will function without false detect inside the +/-30% range of the clock frequency just poses a risk that you might see false lock detect.
2. Yes, any multiple of the clock frequency can cause the false lock detect. Since 1kHz is near the center of the clock frequency it is quite likely that you are hitting the false lock detection described in SLVA778.
Thanks,
Brian