Have you eliminated any electrical/spark problems as a possibility? And if it is a fuel system problem, it doesn't necessarily mean it's the fuel pump. Could be a clogged fuel line, fuel filter. How long have you owned the car? Just thinking about knowledge of service history/how well it was or wasn't maintained.
We need to go back to basics to figure this one out. First, pull codes to see if any are stored, especially relating to misfire. Since most fuel problems don't throw codes (except injector circuits most likely), next step if nothing shows up would be to put a fuel pressure tester on the fuel rail to see if it is within specification. If it is below specs, then you have to figure out if it is a clogged fuel filter, faulty fuel pressure regulator, or defective fuel pump.
There are other possibilities, such as faulty injectors, which you can test by consulting a YouTube video, which will show you both a resistance test and a less-useful "sound test".
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There are other possibilities, such as faulty injectors, which you can test by consulting a YouTube video, which will show you both a resistance test and a less-useful "sound test".