As has been indicated, you can't (officially) use the BBC iPlayer outside of the UK. The BBC doesn't hold international broadcasting rights for its programmes, so the iPlayer servers check the IP addresses of people attempting to use the service and block access from non-UK ISPs.
However several people have reported getting around the block with this:
http://download.cnet.com/Expat-Shield/3000-2092_4-75211377.html
To deal with your actual question:
Downloaded files are likely to be at the highest resolution (with maximum file sizes) but some streamed services (such as BBC iPlayer) allow you to select a lower resolution (using less data).