Get that fixed first and hopefully you'd be fine. If not we'll go further. Get the fan working as it should, check your thermostat valve and check why the PO wired the fan direct. There is no need for the fan to be direct. If the car overheats or something fix the problem. Most probably it would be due to a clogged radiator, just get the radiator serviced and you'd be done.
Start from the wiring of the fan, after that, check why the fan was wired like that, you'd find out the reason soon, find the culprit and replace / repair (which is most probably a sensor or a relay for which the PO didn't bother to buy the original one and opted for a desi method). Check engine light should no more lit up now. If it does, get the codes checked and let us know.
Make sure your fan works on time and turns off properly, and I don't know if your car has a mechanical temp gauge or just a blue and red light or both?