Capabilities of Piwik

If I’m using PIWIK to web analytics of online newspaper, can it give me some meaningful insights with respect to below

o Connection between trending topic and public participation
o Connection between no. of registered users and positive – negative responses
o Connection between no. of visitor users and positive – negative users
o Average navigation time and polling attempts
o Visibility of polling widget – Independent or follow up after articles
o Analyzed response aggregation from a poll to serve as input for content strategy