Timing belt replaced, now it starts rough & check engine light is on

Never once in your story did you say the vehicle when it was in
the repair shop was actually properly diagnosed,nor was any
testing done that actually found any problems

That is & was the main problem

No one has done anything but throw parts at codes

Common sense tells you most if not all of the parts replaced
did not fail,isn't possible at all

You also keep saying the problem-what problem

Codes have nothing to do with replacing parts at all

Codes as used to test systems that set the codes,that doesn't
appear to have been done

You have to know the problem,when & under what conditions it occurs & the broken timing belt may be some how related

Also the vehicle sat for 5 months with old fuel in the tank

You need a fresh start & a new shop that knows how to test
a vehicle

Have these shops actually gone for a road test before & after
any work was done & looked at data & driven 20 miles or more?

Have you driven the vehicle with a mechanic along for the ride
until it acts up,without that, you have little chance they even care
to get involved,at least the parts installers you have been to

Yes,your 2.4 engine is a interference engine,the mechanic should of showed you the bent valves and not installed the timing belt.Did he tell you they were bent when you paid or you found out after you drove home.I would go back and demand money back,if he's won't pay back,go to the BBB and report him and take him to small claims court,your engine is bad.

According to the Gates Timing belt guide this is an interference engine. Have a compression test performed to see if any of the cylinders are down. It may have bent valves or other engine damage if the old belt skipped teeth. Otherwise the new belt may not have been lined up correctly. Take the car to a reputable mechanic and have the cam timing checked and also the compression test done

Are these "mechanics" ASE certified? I ask because it sounds like the stupid things an ASE certified mechanic would do. That patch on their shoulder is there to give people a false sense of security (they also get a chip to go on the other shoulder).

After the fuel cap was tightened, did the Service Engine Soon light come back on? If so, go to an auto zone or other parts store and have them hook up a code reader. They do it for free and you can be sure they wont lie to you.

Doing a belt and AC delete should be simple. Obviously not for some. Even doing the repairs afterwards should also be simple. What may have been a challenge to this mechanic is installing the timing belt. Off a tooth or two and it wont run properly. Many cars today also need special tools for doing timing belts. The mechanic may not have had any special tools and attempted it anyway.

And as for resetting the timing, I'm not so sure it can be done on that car.
1, many vehicles have been DIS (distributorless Ignition System) for many years
2, Many vehicles 96+ cannot be adjusted.

I'm thinking those mechanics are full of BS and may have gotten the timing belt off.

Check the timing belt to see if it is not broken. Fuel pump is behind back seat along with fuel filter. Check cam shaft sensor right end side of cam covers next to the air filter, maybe knocked plug out or loose.

I don't think the rough running had much to do with oil level, since it started running rough a 2nd time. Check the fuel filter and ignition timing.

check your distributor cap may need replacement also other components to check spark plugs and wires good luck

If your timing belt broke, then it is possible that the valves in your engine got bent, which won't allow the cylinders to pressurize the fuel/air mixture, and it will let all of the mix to flow freely into the intake/exhaust manifold. This can be checked with a pressure tester that is threaded into the spark plug opening. A mechanic should have one, or you can probably find one at an auto parts store.

Take the car back to same mechanic immediately

From what you're describing here, the timing belt wasn't installed properly to it's timing marks from the start. You mentioned it ran rough when you got the car back. That immediately told me the timing marks were not correctly lined up. If the belt wasn't tensioned correctly, the belt will gradually start retarding itself to the point of it not running. You did mention that as well already too. In other words, the belt slowly got looser and looser until the valves were not opening/closing at the correct time and eventually the piston hit the valve due to the lack of the tension of the belt not being correct. I really fail to beleive that the tensioner went out "all of a sudden" especially right after the water pump was installed. The reason it is recommended that the timing belt be replaced at the time of the water pump is antifreeze/coolant will SLOWLY deteriorate the belt causing premature wear. This doesn't happen in a week either, this take a long time to happen. My professional opinion is the timing belt was incorrectly re-installed when the water pump was replaced. I've been in the auto repair business for a very long time (28 years) and I have seen this very thing happen when the customer tries to replace the timing belt or water pump themselves especially when there was a lack of experience.