Now draw it without overlapping any lines or retracting the pencil ;)

It sounds like the acceleration on your machine is set quite low, what value is it currently? You should be able to get at least 1m/s^2 comfortably.

In mach3 there is a list linked to from the main screen which explains what each G-code does, so it shouldn't be difficult to work out what the initial commands do and how the arc command has been used to construct a circle.