ok, you replaced stuff that has nothing to do with your issue.

how about plugs/wires/coils???? when did you last change the timing belt.

Roy

I also replaced those when I first got the car, which was about 7-8 months ago; spark plugs, wires, and coil. I also replaced timing belt and fuel pressure regulator. Also, there is this wining noise, I can hear it from inside the car but I can hear it better from the rear of the car near exhaust.

Have the engine compression tested. Do you have overheating and coolant losses issues?
Check the valve clearances as well.

No overheating but I do have coolant loss. But it looks like it's leaking from thermostat housing area. I'll test compression but how would I check valve clearances and what is that?

I believe your engine is equipped with automatic valve lash adjusters so you need not do anything about them.

If your engine had overheated previously, it could have resulted in damage to the head gasket that is causing compresison leaks and would affect cold start and idling issues.

Did you clean the throttle body?
Was IACV new or used unit?

I put in a used, but clean throttle body and iacv is new. I'm not sure if the engine overheated but I do know that timing belt jumped on the previous owner and when I took it apart I saw that one of the lifters were bad so we replaced it. Before we replaced it would barely run. Head gasket recently blew so that was changed also.

Were the valves lapped when the head was removed?
A minor leak in compression would show the symptoms described. btw when testing the compression, do it under cold conditions to be accurate as problem occurred then.

Ok, thanks. The valves were not lapped.

Let us know how it goes.