When I try to take a cookie off the tray too soon it seems prone to cracking later. I suspect that it cracks a little underneath when you lift one side a bit, but looks fine on top. Later when it cools, it becomes less flexible and more brittle, and then it cracks easily. I try to use a very thin spatula, and I always leave my cookies on the tray for at least one or two minutes before moving them. I am sure many different things could be causing it. You could try marking them before you move them, and see if the cracks appear in a place where this problem makes sense. Like donaharrisburg above, I have started smoothing and pressing the top of my cookies flat while I wait, but with a ceramic plate, because I like having a very flat cookie to decorate. I also trim any sides right away while it is more giving.
As far as the icing, I have no clue, but I am rather new to RI. I have noticed that RI transfers I pipe on paper are very brittle, and will break when I try to move them onto the cookie if I am not very careful. Perhaps someone else can weigh in, but I suspect RI is brittle in general. How are you storing them before they crack?