Keep in mind that the page you’re referencing is just guidelines, so just like the page says if you have further questions then contact brandquestions@twitch.tv as they will be able to provide definitive answers if you are concerned. That being said though, using Twitch brand besides a login button or something of that nature should be fine although you should specify somewhere that your game is not in any way endorsed by, or related to, Twitch.
As for your second question, check out https://www.twitch.tv/p/en-gb/brand as that provides assets to use, and guidelines you should follow on how to use those assets and what not to do with them.