Yeah, Saved Messages is that unexpected feature for me too. I also use it to easily send photos from my phone to my laptop. It makes it convenient because Telegram is right at the top in the Share options, and it’s async, so I can send something now and use it whenever.
It can. There's a check box on the telegram desktop to disable compression and on mobile you can send the image as a "file" attachment as opposed to an "image attachment".
