Learn Hardcore Turkish: Ben online eğitim alıyorum.

Because eğitim here is an indefinite direct object. In Turkish, only definite or specific objects take the accusative -i suffix.
• Indefinite: eğitim (some training/education)
• Definite: eğitimi (that training/education)

Why is Ben optional? Can I drop it?

Yes. Turkish verbs carry person endings, so the subject pronoun is often omitted unless you want to stress I.
• With pronoun: Ben online eğitim alıyorum. (I am taking online courses.)
• Without pronoun: Online eğitim alıyorum. (I’m taking online courses.)

What does the phrase eğitim almak literally mean, since almak usually means “to take” or “to receive”?

In this fixed expression, eğitim almak literally means “to receive education” or “to take a course.” The verb almak combines with eğitim to form “to get/training‐wise.”
• eğitim = education/training
• almak = to take/receive
→ eğitim almak = “to take (receive) education”

How is the verb alıyorum formed?