The other codes refer to misfire in cylinders 2, 5, and 7. Add in the backfiring and the most likely cause is spark plugs and wires have been ignored too long. Backfiring can also be caused by burned valves which might show up with a compression test, and for sure with a cylinder leakage test. The spark plugs are relatively inexpensive to try first, and as long as they're out, you can do the compression test. You may be able to borrow a cylinder leakage tester from an auto parts store that borrows or rents tools, but you'll need an air compressor to go with it. It's unlikely you have burned valves in three different cylinders all of a sudden.