To use BBC iPlayer you need to install BBC Media Player, found on Google Play.
The Nexus 7's operating system, Jelly Bean or 4.1.x is not supported by Flash therefore the BBC Media Player application is used to fill the void.
As for the files you are transferring, it could be the fact the N7 uses Media Transfer Protocols (MTP) to connect to a PC so you could try either a cloud storage service like Google Drive or Dropbox. Alternatively try a USB thumb drive, an OTG cable and the app, Nexus Media Importer.
Hope that helps.