My mom just found out she has graves disease, she was prescribed with metropolol succ 25mg, is that what she needs? Is she going to survive?

Yes. Graves= overactive thyroid organ. When overactive, heart rate may go up, metropolol will help this. Next they will address how to caim down overactive thyroid.
Control thyroid. Her thyroid gland has be controlled either with medications, surgery or iodine ablation. Metoprolol is one of the medications used to control heart rate and other effects of high thyroid hormones. Your mother should be fine.