I'm not a native speaker, either, so I cannot explain you anything. I usually pronounce that final "r" like the British (that is, I don't pronounce it unless it's before a vowel). As for the word "here" and similar words, I do likewise. So, for example, in "here it is", I pronounce the "r", while in "here" alone or in "here comes", I don't. In the case of "here you are", I'm not so sure. I do pronounce the "r" in that case ([hier]), probably owing to the fact that the "y" seems to be a vocalic sound (is it?) So I should say that the case of "here" is the same as that of the words ending with an "r": [hier] before vowels (in my opinion, that includes "y"), and [hie] everywhere else. But, as I've told you, I'm not a native speaker, so don't rely completely on what I've said.
Here in Spain most people pronounce those final r's, too. There might be two explanations for that: either it's because of the huge influence of American English everywhere, or because we have a tendency to pronounce everything as it's written (so if we see an "r", we utter it).