Epoxy will not attack most foams but Polyester Resin will. If you use the blue or pink foam you can shape it easier than some others. Usually best to go in one direction...Right to Left, etc. not back & forth... I reduces tear out. The board you referred to is called a parting board...designed to create a female mold for the fiberglass to be created. You make one side then you clean it up and then make the mold the other side. Usually people will do wet seams in the mold for the two parts after the fiberglass is laid up on both sides when they bolt the halves together. Takes some practice and you make some small rollers to work the overlap from one side to the other inside the mold. The other option is to take the two halves and trim them after they are cured and then you seam them from the inside after they have come out of the molds.
You won't be using 5 minute or 30 minute epoxy if you want to do any composite work, even with thinning it down. You need a slow hardener suitable for the temps you will be working in. Making a hot box to heat cure the fiberglass can be beneficial for some epoxies. They are a foam board (1") box over a bench setup with a few small light bulbs for heat source. You need a thermometer you can view what the temps are in the box without opening it of course. Some folks rig up thermal switches to control the temp between a high point and a low point for the on-off cycles. Once it is up to temp it doesn't take as much on time or wattage to keep it at the elevated temps if it doesn't have holes for the heat to escape. The use of vacuum bagging is also done. You can make a vacuum bagging pump pretty inexpensively, believe it or not, with a medium sized aquarium pump, coffee, can, some brass fittings, and a board... It will pull a vacuum in the mid to high 20s.
The reason people make a mold is because doing so allows you to have a much smoother surface than doing the layup on top of the foam. Unless you don't care about putting lots of plastic filler on it (not recommended as it will show itself before too long.
David