welcome to the wonderful world of camping!
next time, try to store your tent indoors, away from the elements, and always make sure you pack it away when its dry and clean. if thats not possible at the end of your stay at a camp site, then loosely pack it until you get home and can clean and dry it, then pack it away properly.
to remove the mold and mildew, people have had success with tile-x products.
as for the holes in the screens, ive seen screen patch kits around. a long time ago i patched a friend's tent screen. i used a section of screen cut from a destroyed tent and sewed them together with some nylon thread. came out great and last i heard the patch was still holding strong!