Is it possible to download all Wikipedia pages of one category (for example, http://en.wikipedia.org/wiki/Category:Births_by_year) and all it's subcategories?
The problem is that specific page are not tagged with topmost category and per page trace with Wikimedia API is very long. May be it is possible to download this in bulk with some tool?
No, it's not possible, because of how categories are made. You have to walk the categories yourself. See also a discussion at http://lists.wikimedia.org/pipermail/analytics/2013-December/thread.html#1368
For the specific category, you only have to use Special:Export and add the category in it instead of a list of titles. Assuming you meant wikitext export for "download"; if you want HTML, your only option is the render module in the API, or parsoid.
