Will iPad2 app work on iPad3?
Yes, it will. The iPad 3 has exactly twice the pixel density in each direction as the iPad 2, so the OS will just go ahead and "scale up" the graphics (except those which are made from images in the app - you'll have to generate a higher resolution version of these image files for iPad 3).
Do we need to develop separate app for iPhone 5?
Not a separate app, you just have to pay attention to the different screen aspect ratio. If you don't do that, you'll have black bars at the top and the bottom of the screen.