I would like to build another room in the unfinished part of my basement BUT I would like to move my washing machine and dryer to another unfinished part so I can use the windows in the room and then only have to build 1 more wall. Does anybody know how far away the washing machine/dryer has to be from the electrical box, furnace and water heater?? As well... any idea how far away we would have to build the other wall from these same items?

Codes vary locally regarding furnaces and water heaters. To be accurate you need to ask your local building inspector this question. They can safely be in proximity but codes will address the exact distance. Is the dryer gas or electric? Do you have a GFCI circuit or receptacle for the washer?