It could, yes.
Yes it will, plus loss of power, & poor mileage.
Having no catalytic converter installed is illegal and can cause a myriad of problems. Probably not a backfire though.
Yes, internal coolant consumption can damage a catalytic converter.
A clogged converter will cause an extreme loss in power, poor mileage, and hard starting. If it is clogged really, really, bad it may cause the engine to not even start.
No, the catalytic converter is downstream from the EGR valve so it has no effect on it.
Yes
No, the catalytic converter has nothing whatsoever to do with your defrost system.
A bad catalytic converter can cause hard starts if it has become clogged. This produces excessive back pressure in the engine.
Modern cars use two oxygen sensors to monitor the exhaust before and after the catalytic converter. Removing the catalytic converter would cause your engine to run improperly, possibly causing damage and most likely making your gas mileage worse. Just replace it if it's broken.
A bad coil can damage a converter. If the engine is misfiring, it will cause raw fuel to get into the converter and that can cause failure.
No, there are many other parts on the engine that can affect mileage but the catalytic converter is a passive device and, if new and clean, cannot affect the way the engine runs or the mileage it gets. Think of it as a filter, althought it's actually a lot more complex than that, if it lets the exhaust gases flow throught without any major obstruction then it can have no effect on the car's performance.
Yes