Does EKG indicate brain death?

yes

It slowly shuts down when dead.

According to halakhah (Torah law), the deciding factor in death is presence or lack of a heartbeat.

it is dead and that's it i think I believe they say that under normal hospitalized conditions, your brain can survive 3-5 minutes at the time of cardiac arrest.

(And ask questions? - sorry, I couldn't resist.) Seriously: brain death (originally a legal term) by definition means, an irreversible, final (and terminal) cessation of all brain activity. Including...