Mitsubishi Galant over heating with battery light and brake light on

Battery and Brake Light on simultaneously on most Japanese vehicles generally means a bad alternator. I owned a 2003 Galant with the same engine and had the same issue.

Most Retail Automotive Parts Stores will provide a charging system test for free.

The Gauges indicating improperly are likely a separate issue. Gauges malfunctioning and blown fuses would lead me to worry about electrical health. I would start by removing the electrical grounds, cleaning, and reattaching them.

As another user mentioned, make sure that you have the proper level of coolant, and that it's circulating properly. Bring the vehicle up to operating temperature and check the temperature of both the upper and lower radiator hose, either with a non-contact Infrared Thermometer or by feeling the hose with your hand (exercise caution for moving options excessive heat etc.)

Here is an article at YourMechanic.com which gets into How to Diagnose Cooling Issues If you do have an issue where both hoses never get warm, even after the vehicle is at operating temperature, then you should continue with some of the other components covered in that article linked.

I hope this helps.

Like four months ago the same thing happen to me on my Mitsubishi Galant 2001. I checked everyrhing and it was the altenator and starter that they were bad and damage also the battery. I bought a new starter, altenator and battery and everything was fixed. But tonight coming from the movies, the brake and battery light turn on and the thermometer went up and down. I get home and leave the car in the garage. Hope is not the same, what you think guys.