Topic on Extension talk:Cite

Does the output follows any citation standard? Is there a possibility to switch between citation standards?

I'm afraid this question isn't specific enough to give a comprehensive answer. Maybe you are looking for en:Wikipedia:Citing sources?

Well, on the side of Wikipedia you can modify how the references look in References paragraph via template. But can you modife it in the text? E.g. insted of having anchors lik [1], use somethig like (Peters, 2015)?

To some degree this is possible: en:Help:Footnotes#Footnotes: groups. The section en:Wikipedia:Citing sources#Parenthetical referencing describes some more possibilities similar to what you are looking for.