From time to time acts like it is not getting fuel and tries to die out while driving. Recently, I smelled gas when I started it up. I had it checked out and so far no problem has been found.

Question edited for clarity, punctuation and spelling.

There are lots of ideas here, but due to the fact you can smell gas, clean the Throttle Body with spray cleaner. It isn't shutting properly. Clean the MAF (Mass Air Fuel) sensor as well.

https://www.cargurus.ca/Cars/Discussion-t24292_ds857944

Lots more here

https://www.google.com/search?q=2003+Nissan+Murano+stalling+and+jerking

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Check fuel filter.

have you checked the cylinder compressions as backfire and blue smoke can be a symptom of low compression , either rings or valve seats but would need a dropdown test to be sure

when you crank it, do you smell fuel? if you do, you're getting fuel so try replacing the distributer cap and even the plugs. if no gas smell, the fuel filter needs changing or the fuel pump is bad.

Check to see if the VAT is causing the hassle and shutting down the ignition after it starts.

First check fuel pressure and see if is to spec, some times the new pump is to much or not enough. Just double check they gave you the right part. make sure you hook every thing like it was so back track your work. Make sure your filter is on right seens you smell gas and all lines are right on

very possible the fuel pump. have fuel pressure checked.

we call these vehicles exploders.. lol
sounds like a fuel delivery issue, does it throw a check engine warning?

Most likely a lack of fuel, check the fuel filter first.

sound like to me that u are getting air from somewhere one of your lines may be cracked or not tighttend all of the way or you may have overtightghted one of them