Al Jazeera is certainly funded by Qatar.  
It's also true that the BBC certainly played a role in helping them become a public broadcaster.  

I have heard there is a distinction between the Arab and English versions.  I suspect that may well be true - but I don't speak Arabic and watch the English version and it is a fine broadcaster that covers parts of the world "we" in the west only bomb and don't understand.  It also does some amazing human interest coverage in various parts of the world. 
 I sincerely hope it does not go dark as a result of this schism.