Yes, an insufficient C rating can lead to battery cell/pack damage. Other causes of cell/pack damage are: stalling the motor with the throttle "on", improper battery maintanance, and general abuse of the power system (i.e. allowing the pack to sit for extended periods of time without charging, overheating the battery due to excessive loads, etc). Please note that I am not accusing the owner/operator of abusing the system. Other causes of battery/cell damage would be internal or external shorts that drain the cells beyond recovery.
Mixing old and new cells, while not always the best idea, can be done as long as the every cell has the exact same voltage and capacity ratings.