The 'now', emphasises 'at the present time', and therefore additionally suggests that the situation has changed recently. 'I have now been horse-riding seven times'. Here, the 'now' suggests that you have recently been horse-riding, and that recent excursion has bought your count up to seven. Amanda is correct that in simple cases, you would not use it, but in this case, her alternatives simply do not work.

I'm a native English speaker, and I probably wouldn't say "have now been." I think that adding "now" is probably an attempt to emphasize the recentness of the activity under discussion and I would probably indicate that by saying, "Recently I have been..." or "Now I am _____ing (dancing, eating, trying, etc.). But it is just an emphasis. What I mean is: The verb "have been" indicates present activity that the adverb merely emphasizes.

There's no difference, "now" acts as adverb here and you can flexibly put adverb in a sentence.