Will using female/male connectors to connect a stereo to a cars factory wiring degrade the signal at all?

Answer 1

If they are quality connectors, ie. not a $5.00 special, they will not degrade the signal. Also, as long as they are line level (directly powering the speakers) the signal is strong enough that you can use the cheap ones and not notice any difference. Preamp level wiring is the only time you really need to be concerned, because the signal is weaker.

Answer 2

no but don't cut those wires .there are adapters that are sold and they connect to the stock wires .
you can splice into the wires if necessary but keep the plugs intact .
mainly keeps the value up
easier to trace th wires