I haven’t read that far yet, so I don’t know the context, but I can answer for the conjugations.
Passive verbs are made with the conjugation られる in Japanese. 壊れる→壊れられる
壊れてる is most likely the spoken form of 壊れている, which you are probably familiar with, that means “is broken”.
edit: if you are ever unsure about conjugations I can recommend this tool that I used when I started learning Japanese http://www.japaneseverbconjugator.com