Does the number of traders directly affect the volatility of the market?
Yes as it increases the demand.
If it does, can we assume that trading was easier before with less traders (less volatility) than now when there are more traders, and the market more volatile?
Pretty much because the demand wasn't that much before. But we can also think of having few traders in the market but most of them are likely the whales. They bring so much demand that even they're less, they also contribute to much volatility.