Actually no. Age of a web page does not matter but when any new page is created like a thread in forum or news in news site or even a blog post the page takes time to get indexed and ranked based on the links ( internal / external ) to that page and that may give an impression that its an age of a page as a factor.
I don't think so. In an interview Matt Cutts brushed aside even the importance of age of a domain saying "We want quality information, not old information" kind of words. I think that answer is kind of stupid though.
the main thing if you are an authority site or not.....no matter if you have a relatively old domain but at the end your content does matter. So try to become an authority in your niche..