No, you should pull the fuse for the stereo per the previous instruction, charge the battery, preferably with a low amp charger overnight, start the car in the morning and see if the battery light on your dashboard is lit. If it is not, you should run the car in the driveway with every appliance and light and whatever on and turn the car off after an hour and let it cool all the way off and try to start it.
If it seems sluggish turning over or just clicks, replace the battery (yourself), drive the car to a mechanic and check the alternator (or if you can do it yourself, remove the alternator and bring it to a parts store or chain that can bench test it).
Keep the stereo until you do these things. Your aftermarket stereo's weirdness is probably the result of a bad battery and alternator, not the problem.
The lights that are staying on are LED and should take a week if the car was sitting in cold weather to make a difference. I bet that you need to change at least the battery and maybe or the alternator, and when you do the stereo will go back to normal.