Learn Russian: Он очень болен, поэтому жалеет себя.

The word себя is a reflexive pronoun that reflects the action back onto the subject, meaning "himself" here. If you used его (him), it would mean he pities a completely different person! You must use себя whenever the subject and the object are the same person.

What case is себя in this sentence?

It is in the Accusative case because it is the direct object of the verb жалеть (to pity). Remember that the reflexive pronoun себя never has a Nominative (subject) form, and its Accusative form looks exactly the same as its Genitive form.

Why does the sentence use болен instead of the regular adjective больной?

болен is a short-form adjective. In Russian, short forms are often used to describe temporary conditions or states. By using болен, the sentence focuses on the fact that he is currently sick right now, rather than being a chronically ill person.

Both потому что and поэтому relate to cause and effect. Why use поэтому here?

потому что gives the reason ("because"), while поэтому gives the result ("therefore" or "so"). In this sentence, the sickness is the cause and the self-pity is the result, so we use поэтому to link them.