Nope. You can just link to external videos though, I'd suggest Streamable if you need to upload something quick.
Not sure. I think videos would be very expensive on the servers so I wouldn't expect it anytime soon. For now I hope they'd just add better embedding support so you can watch videos without leaving the website.
Honestly, I like it better this way. Exactly for the reason you just pointed out, costs. But better embedding capabilities sound good. (Disclaimer: I honestly don't give a fuck about videos in social media, I prefer images, and maybe gifs)