As far as grip width goes, people with longer arms will have a wider grip and people with shorter arms will have a narrow grip. Other than that it's more of a comfort thing.
Your 2nd pull definitely needs to be more aggressive. It doesn't look like you have much of an issue in the receiving position, you just jump back a little bit on the clean.
Rather than staying over the bar longer, it looks like you need to shift your bodyweight back towards the back of the foot more on the first pull. Also, like Ben said, push that bar into your body more before initiating the 2nd pull. Try doing some Halting Snatch/Clean DLs and focus on keep your weight back and using your lats to push the bar all the way into the hip/thigh.