For 1 and 3, 'the' tends to suggest all, or perhaps more precisely, the lack of 'the' implies some.
For 2, the presence or absence of 'the' doesn't really imply anything, strangely enough.
For 4, 'I don't like the reviews on this site' would suggest that you have looked at some or all of the reviews and generally disliked them.
'I don't like reviews on this site' would suggest that you prefer that the site not have reviews at all, in principle, suggesting nothing about whether you had looked at any reviews in particular.
For 5, 'I read books by John Summers', it's a bit complicated. Consider the tense of 'read':
In the present tense, 'I read books by John Summers' means that you have read and generally plan to continue reading some or all of his books.
In the past tense, 'I read books by John Summers' means that at some point in the past you read some, but probably not all, of his books.
In the present tense, 'I read the books by John Summers' is not something a native speaker would say, but 'I am reading the books by John Summers' suggests that you are talking about a set of books including both books by John Summers and books by other authors, and you are reading some or all of those by John Summers and excluding those by other authors.
In the past tense, 'I read the books by John Summers' it would also suggest a larger set from which you have read his books and excluded those by other authors.
Best Answer
It's a joke. Vodka is well known in the West as a Russian spirit, even as a stereotype of Russia. Skyy is saying that their vodka is so well filtered, they removed something that no one would have thought would be possible to remove from vodka (i.e., its association with Russia). That's all. If you start looking for alternate definitions of "Russia," or find it meaningful that Skyy is made by an Italian company, you're overthinking it.
"The Russia" is not normally acceptable, as you note, but it follows a widespread pattern of pairing "the" with unexpected words in informal conversation for effect, as a form of metonymy: wipe the smug right off his face.