Nothing I can do about the red x thing. That's between Tapatalk and the forum admins. But you can still just click "reply" and view the images, then cancel the reply. It's an annoying workaround, but a very simple one.
I suspect there is some fairly simple setting or database entry of some sort that didn't make it to the new server. Note that you aren't getting a browser-default "this image doesn't exist" icon (which usually looks like an embossed rectangle), but rather a replacement image inserted by either XenForo (more likely) or Tapatalk (less likely). Quoting it makes the image appear, so obviously the image was correctly uploaded and is fully accessible on Tapatalk's server.