First, in corona you don not have one object displayed multiple times, thay can be the same type or have the same texture but each one is individual object.
Question is too vague. When you begin selecting object, when you end selecting, when you move objects? You must answer those questions yourself first.
Always thing about corona as empty canvas, not as set of ready and fixed elements with special functions. You want object - draw your self. Want object to follow finger - think how to make it aware you are touching screen, that you are toching object, when you begin selecting and when you end it. Want to move multiple objects - take each one of them and move each one or put them in group, move group and free them from group at the end. Always think (if possible) as you would do actions on piece of paper with eg scissor-cut images and objects. Divide and conquer/win - divide big problem into a small and basic ones and by solving each of them solve general problem.
As such Corona is not interface oriented (mainly - there are some native features but few only) - in this way that there are no combo boxes, native buttons, scroll views - Corona gives you canvas and tools to draw to you so you can do as you like.
May ask what with widget library? Corona guys just used canvas and with use of images, functions and events they created buttons, scroll views etc. So you must do things this way. Corona is freedom to create things as you want 