The Charter covers "UK Public Services" and the "World Service", as does the Agreement with the Minister of the Crown. The World Service is a specific thing, which you can read about for yourself.
* So public service broadcasting to other countries isn't within the terms of the Charter.
* Commercial activities are prohibited to the BBC itself. They are limited to commercial subsidiaries.
The upshot of this is that services that you get outwith the U.K. are not from the BBC. They are from commercial subsidiary companies, such as BBC Studios for example, or from joint venture companies. BBC Studios is what broadcasts BBC content such as BBC America outwith the United Kingdom. Similarly, the WWW site that is served up to computers outwith the United Kingdom isn't provided by the BBC. It is provided by BBC Global News Ltd, another commercial subsidiary. It's quite different to the WWW site that is seen within the U.K..
The commercial subsidiaries aren't funded by the Licence Fee, and the BBC itself is not permitted to make a profit from its dealings with them, which must be "at arm's length" (to quote the Agreement).