Are “humility” and “humiliate” related?

Yes. Using tools from Online Etymology Dictionary:

Humilis is Latin for humble. Humble is Old French humble < *humle < *humile < humilis.

Humility is from Latin humilitas “humbleness”, which comes from humilis.

Humiliate is to make someone feel like crap: you’re humbling them, you’re making them feel low (which is actually what humilis originally means: lowly). Humiliate is a back formation from humiliation, humiliatio in Latin, which is derived from the verb humiliare “to make humble”, which comes from humilis.

It turns out Middle English used to have a verb derived straight from humiliare: to humily “humble oneself”.