Does the Daily Prophet report news about what happens in other countries? How do the Wizards in Britain know about what happens in the Wizarding world of other countries?
Yes (at least regarding Quidditch)
The sports column of the Daily Prophet would cover international Quidditch (or at least during the World Cup season.)
You can read a collection of their articles from the 2014 cup here1, written by sports correspondent Ginny Potter.
To quote a random passage:
Ivorian Chaser Elodie Dembélé, aged only 18, scored seven of Ivory Coast's ten goals. Norwegian Seeker Sigrid Kristoffersen out-raced her counterpart Sylvian Boigny to take the Snitch in the 128th minute.
NORWAY VERSUS IVORY COAST, Sunday Prophet, April 13th 2014
1. Screenshots from the old Pottermore. These were some of the stuff lost when Pottermore "upgraded" their website,