Unless you are playing Aric's mod, there are no Harpy eggs.
Pregnancy without mods is simply a matter of having a penis cum inside a vagina repeatedly. Only contraceptives will prevent it. The note for the infertility trait explains in detail: https://strive4power.fandom.com/wiki/Traits#Infertile
Obedience can be gained a lot of ways: item daily bonuses, meet interaction (mood bonus), high loyalty, lock them in jail with a Jailer, or have a Head Girl assigned (requires 8 slaves). If you use a Head Girl, be sure to change the job setting in Mansion Settings to either Strict(uses confidence) or Patronage(uses charm).
Edit: clarified Head Girl