Vclaw
2
You can use the fee tag for whether something costs or not. ie fee=no or fee=yes or maybe specify it, eg fee=£1
The wiki page http://wiki.openstreetmap.org/wiki/Tag:amenity%3Datm suggests tagging it with “cost” instead. But I think this is non standard, some discussion on the talk page suggests just using the more common fee tag.
I don’t think there is any specific tag for internet cafes. But there is an internet_access tag: http://wiki.openstreetmap.org/wiki/Key:internet_access
So you can tag it with amenity=cafe and internet_access=terminal