No,the remote start wires should be not be cut off because this will cut off the 12 volts DC from battery supply of the engine of the car. If the problems continue it's better to check up the car to the autoshop or buy a new one.
No. More than likely you car is a gm product or another make with a security system. Your best bet is to get a mechanic involved who understands auto electric systems.
You should cut them only if they make a break from the battery to the starter.A small jumper wire could be used to make sure that power is still going to your starter before i would recommend disableing the remote start feature.
No. Do not cut any wire or take anything out yourself unless your the person who installed it in your car. It sounds like your having electrical problems and these can be trick so i recomend you take your car into a licenced mechanic to try and find the problem.
I would not cut those wires unless you know for a fact that is causing the problem and then only in an emergency. You are best advised to get a qualified mechanic to look at it.
No need to cut the remote start wires. 1st Cheack your Battery wires. Mostly it will start with battery neck only. After checking it give a try. Still cant start it know, better check the fuel injectors.