Learn Italian: Il bambino cade e si fa male. - The child falls and hurts himself.

In Italian, the expression for "to hurt oneself" is the reflexive verb farsi male (literally, "to do harm to oneself"). Because the subject is il bambino (he), we use the reflexive pronoun si and conjugate fare as fa.

How would I use siccome to say "Because the child falls, he hurts himself"?

You would place siccome at the very beginning: Siccome il bambino cade, si fa male. As taught in this lesson, siccome is used to introduce a cause when it sits at the start of the sentence.

Can I use perché instead of siccome to connect these two actions?

Yes, but perché usually goes in the middle of a sentence. You would swap the order to say "The child hurts himself because he falls": Il bambino si fa male perché cade.

How would this sentence look in the past tense?

It would be: Il bambino è caduto e si è fatto male. Both verbs use essere as their helper verb in the past tense. Cadere (to fall) uses it because it is a verb of motion, and farsi uses it because all reflexive verbs take essere.