When driving on a hill or down slope engine will suddenly shut off

So to be clear I have been pretty sure that my gas gauge has been lying to me for the past month because there is no way every time it says I am below a quarter of a tank that it only takes six to seven gallons when you have a fourteen gallon tank approximately. (I do not know if that is actually related to the problem, however, I thought it needed to be said). Okay, so randomly (or on a hill nine times out of ten on the downward slope) my engine just completely shuts down with no hesitation or warning. So I do not have time to get out of the way of traffic. (Keep in mind I have another car that stalls a lot so I know that is possible to have a little bit of warning). My check engine light rarely comes on after these events but after it happens it usually takes five or six cranks to get started and running. It will try to start and you can hear it get started and then give up many times before it finally turns over completely. I have also notice that occasionally my rpm's go haywire and I mean like going 40 and my rpm's are over 4,000 when on the highway I can go 80 and not be over 3,000 rpm's. Now are all these things correlated or is it that it is getting close to winter and my car just hates the cold (my main cylinder and three of my brake lines broke last fall right before winter so I had to drive a different car until we were able to fix it) and breaks more often. I do not know, but does anyone have any Idea why this might be happening?