2004 Mazda 3 stalls and is hard to start shortly after filling the gas tank. Secondary problem is the abnormal loss of oil every week. No blue smoke, but the oil is going somewhere. Are these two problems related? What are the possible solutions?
These problems need to be attended to, and the questions asked of your mechanic. In normal operation, none of those things are connected.
Is this just one fill up you’re talking about? Is the engine easy to start, or restart, at any other times? Are you ceasing to pump gas as soon as the pump automatically cuts off? You should. If you don’t it can cause problems with the EVAP system.
Your mechanic will look on, under, and around the engine/transmission for oil leaks. It could be something as simple as a leaking oil filter.