Do I need to start a new game to use my own designs?
In order to use designs you made in the out-of-game ship designer, you need to start a new game, yes.
Do i need to add the modules as I design the ships or can I add the modules during the game as they become available?
Putting the modules on the design means that you'll need to wait until you have researched all of the needed techs before you can actually build the ship. Otherwise, it makes no difference.
