Car backfired and lost some power

There might be enough oil getting past the rings that it is causing mis firing. Is there smoke coming out of the exhaust when you get on and off the gas? That is a sign that the engine is not burning all the oil and combustion is not complete. I am giving you a walk through on backfires to help you understand and diagnose the issues as it covers the most common problems. Just use the link below;

https://www.2carpros.com/articles/engine-backfires-while-running

Check the fuel injectors with a noid light. Just a 12 volt bulb with positive and negative leads. Touch them to injector leads and turn engine over and if it lights up injector is okay. It might be clogged, so if I did not mention it a can or 2 of quality fuel system cleaner will do wonders. BG44k is the best but you have to get it at the parts counter of car dealerships and its $20 a bottle. Sea Foam is easier to get and a good second choice. You might experience rough engine performance when you use it as it removes deposits which eventually settle in the oil pan. So, after 2 tanks of gas, each with a bottle, then one tank of gas after that be prepared to change the oil as it will get dirty.
If your fuel filter is that old it is certainly adding to the issue if not causing it. That may fix your problem.

Yes run another can and then run an entire full tank of gas after that before you evaluate performance. However I think you still might want to check injectors. Below is a link to an extensive test of fuel injectors. It will explain symptoms, which are quite like yours but you should still run cleaner and replace filter, and tell you procedure to test injectors. Just click link below;

https://www.2carpros.com/articles/how-to-test-a-fuel-injector