There's no ideal number. No matter how you do it, innocent people will be put in imprisoned and guilty people will go free, so you're just making an arbitrary trade-off by defining a limit. Though I like the way it is in the US: you can only be tried once for one crime (except for the civil suit when there is one).

I heard the law was to prevent some sort of corruption/exploitation, but I forget exactly what. I think it was to prevent people/the system from being abused for political reasons. I lean toward mercy when it comes to law enforcement and punishment, which is why I prefer it to be one time. Better not to have something hanging over you your whole life (or as long as the statute of limitations lasts, I guess) and better for 5 guilty people to go free than for 1 innocent person to be imprisoned or even executed.

Difficult to answer. How many times should a convicted person be able to bring forward new evidence to correct a false judgement? After years new evidence based upon new forensic science can change a judgement fundamentally. In cowboy countries they give a damn about truth, fight is all and god is the only judge. In more civilised countries we reevaluate and evaluate evidence and try our best to come as close to the truth as human effort can bring us. But, big but, grinding a soul many times through the mill stones of justice can be a crime too. I do not know where to draw the line between too many and too less. Human efforts are so limited and in vain too often. But keep yourself away from simple desires of revenge and hate. It darkens your own soul in the end.