not sure but maybe has to do with patents(?) since most companies can hold 20 yr patent terms on thier products in USA and they decided to went with the better side of "why not open this thing up? we already made some money out of it"
Not really how patents work. It does not matter if the code is open or not, others are still not allowed to use patented code elsewhere or at least not commercially. (Not talking about the legitimacy of software patents)
I'd imagine so, it's an d game, not sure how much they're still making in it (not much I'd guess given the rampant hacking concerns and protests I've seen online)
So... Why not do the cool thing and open source it for the community to maybe build something cool in it (hell I'm SURE someone will make some neat stuff)
Usually valve releases boxes with skins for summer, halloween and winter. I dont know if some are made by valve or all are community created with a cut for the creators. But it seems a low effort way to keep making money out of an old game.
And TF2 is still extremely popular, both with high player numbers, active content creators, community tournaments and the like.