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Backfires indicated a bad air/fuel mixture. There are couple of things that will cause this. You should start with the basics.
However the main test that you want to do here is going to be a fuel pressure test at the rails. This will not only test the pump, but also the fuel pressure regulator. Also make sure all you injectores are working, if you put a screw driver on a fuel injector you should feel a ticking.
You can chec if a muffler or catalytic converter is clogged by hitting them from the bottom. You should hear a rattle in them. You can also take off a oxygen sensors and flow air through, this test is a lot better, there should be no restriction when you blow air through the oxygen sensor mounting hole.