Learn Spanish (Latin America): El superviviente empezó a enloquecer en la isla. - The survivor started to go mad on the island.

Both words mean survivor and are completely correct. In Latin America, sobreviviente is generally more common in everyday spoken Spanish, while superviviente can sometimes sound slightly more formal, literary, or Spain-leaning, though you will easily be understood using either.

Why do we need the a in empezó a enloquecer?

In Spanish, verbs that indicate the beginning of an action, such as empezar or comenzar, always require the preposition a before a following infinitive verb. Leaving out the a is a very common trap for English speakers!

How is the verb enloquecer formed?

It is built from the adjective loco (crazy/mad). Spanish frequently creates verbs that mean 'to become [adjective]' by wrapping the root word with the prefix en- and the suffix -ecer. Another common B2-level example is enriquecer (to get rich) from rico.

Could we use the imperfect empezaba here instead of the preterite empezó?