Are knights vulnerable to spearman?

Spearmen have a bonus when fighting mounted units, same as Pikemen. However, Spearmen and Knights do not show up in the same era - Knights and Pikemen are both medieval units, while Spearmen are ancient units. This means that Knights are relatively more powerful than spearmen, even taking into account the bonus vs. mounted.

To compare: Spearmen are strength 11 with +50% vs mounted units. Vs. a Knight, this puts them at 16.5 (before other bonuses). Pikemen are strength 16 with +100% vs mounted units, giving them a strength of 32.

Since Knights have a strength of 20 (since nominal unit power increases with era), they will beat spearmen despite their "vs. mounted" bonus.

Yes, knights are still vulnerable to spearmen. Spearman have a "50% bonus vs. mounted units". Though, spearmen have less strength than pikemen, so they won't be as effective. Spearmen may still be useful against knights for reducing their health, even though they are overpowered.