No. Exactly we cannot say that Nokia 8110 4G is a waterproof device. But it is IP52 certified. Means it is splash proof. You are protected up to some extent by water.
Nokia 8110 4G comes with 1500 mAh battery to support the heavy requirement when you want to use the vibration function of the phone. The vibrator is strong enough even if it is deep inside your handbag.
Yes, Nokia 8110 4G does have the FM radio.
Yes, Nokia 8110 is made of Polycarbonate material, which does not allow power transmission and thus it makes a shockproof mobile phone.