In terms of grammar the language is the same in all parts of the world (especially written language). Ukranian accent does exist though, and there is some risk that you might develop Ukranian accent if noone corrects you. This applies to spoken language only. Some vocabulary derived from Ukranian may also be present in the area you are staying (but i don't think too much; though ideally it's better to know that such words are derived from Ukranian or part of that local dialect). The biggest difference and issue here is Ukranian accent I think. It applies to some characteristic sounds.
The newspaper language is the same. Makes no difference what you read. The newspaper editors are supposed to be professional speakers of Russian, so a Russian newspaper with pure Russian in theory may be issued in any part of the world.