NewspaperTaxis: A lot of nationals (the tabloids in particular) pay people to keep an eye on local newspaper stories that they can recycle. You'll notice that Mail Online, for example, has a lot of school uniform stories - I'm pretty sure that in at least 90% of cases this will have been a local newspaper story that the Mail then picked up.
Mail Online also lifts a lot of stories from other nationals, some with acknowledgement, some without. The Mail (paper rather than website) also, rather curiously, has a syndication agreement with the Guardian, or used to, at any rate.
And it's an interesting point about months after the event - Mail Online is always on the search for new content. You'll notice the front page refreshes constantly. So if it comes across a story that's months old, it will happily recycle it unless it's very obviously out of date.
It's worth making the distinction between Mail Online and the Daily Mail - same brand, but different editorial teams often publishing very different content.