Hazard light is on all the time when car is running and shut off

Hello, sounds more like an anti-theft system concern / activation causing the lights to flash more than a hazard light concern. Have you tested the battery in the first place -- verifying it is fully charged and able to handle a load? If the battery is marginal or failing, it can cause all kinds of voltage related concerns with various electrical modules. On a 21 year old BMW, or any vehicle, anything is possible. Testing will be required to see what is staying active when the vehicle is off, resulting in the battery draining -- indeed -- if the battery tests good in the first place.