Oil should not be dripping from the engine. The engine should not be stalling out. Those are signs that something is wrong. A potential engine failure.
Many things can be wrong, but many can be fixed relatively inexpensively if they are taken care of when they are first observed. Continuing to drive the car around and counting how many times it stalls one each 20 mile trip without having a good idea what the problem is may lead to a much more expensive condition. Stop driving the car unless you need to take that risk.
The picture and video do not show enough information for anyone to do a good diagnosis. I bet that 'Blue62' can advise you of a proper order of things to check for initial troubleshooting, but if you are not comfortable working on engine parts, it needs to go to a shop.
