In terms of data being collected and sent back to Zack's Mohawk Limited, at present we collect absolutely nothing. There will be some non-identifying information sent to us via voluntary error reports, but this only contains information helpful to identifying crashes/bugs.
GrappleApp needs to download the move sequences separately from a large .zip file, which requires the network connection permission. This is then unzipped inside the application and does not impact on your external storage or SD card.