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The duplicate content issue is more of a negative than a positive in regards to creating a larger indexation rate. If these are useful to the user and build the relevancy of your site structure and content, add the "noindex, follow"- like Chris Holgate said.

Hi Irina, Meta keywords are unlikely to cause a penaly and are simply ignored. So you can do them but it's probably a waste of time. news_keywords only works if you are an accepted news source in google news and it's likely that this will only effect news results. This tag was created to give journalist more freedom with their headlines so they don't have to keyword stuff the headline. It's meant to lead to a more natural looking article while still giving an option to give some keyword indication of the theme. Hope that helps. Mulith

I don't think ajax used in a search boxx will affect your site Unless you are using ajax in a module/widget on every page for content and changing that content then maybe but I am not  sure. As for your other metrics you can use heat maps and surveys to see that.

That's a tough one, huh Irina? If sites are only agreeing to link via payment, I'd try to add some value by looking for content sharing opportunities and slightly more robust ways of purchasing an associated link than just the link alone. This way there's some justification to the payment and the link can be considered residual.  It sounds like you're doing all the right things so far.