If its between apple and android you can't - if it's between apple and apple just download em again they're free if you paid once - and the same goes for android
No you dont get charged again. If you hit the left key you get a number of options one of them being MY APPS. selecting that will show the items that you have downloaded/paid for. and you can download them again if for any reason they are not on your phone/memory card.
There is also an app called app2sd or apps2sd, and it allows you to transfer the downloaded stuff to your memory card assuming you are using one?