Many write ups and videos online say when you align the camshaft pulley's marks to TDC, the oil pump should also be aligned with its marks. But when I set the camshaft to TDC, the oil pump marks are almost half an inch off and I don't know if I should reinstall everything how it is since the engine was running fine before hand, or if I should align the marks...

Thanks

 

The timing marks must be aligned properly, otherwise the pistons will hit the open valves bending them. That will require a head rebuild or replacement.

Reset the timing belt. Verify the slack is taken out of the belt. Rotate crank to verify timing stays.

If an F22* engine, the below diagrams show how to properly align the upper cam and lower crank sprockets.