A:AnswerYes. It will fit the new Hero 7 Black. I am using this for the H7Black. In fact, Hero 5, 6 & 7 have the same body so the accessories are interchangeable including the battery.
A:AnswerYou don't need the Sleeve to connect a GoPro to a tripod. You would use the Frame that came with your GoPro, and you'll also need an adapter (look for the GoPro Tripod Mount) that converts the screw on a standard tripod to a GoPro connector. If you're using a GoPro tripod though (like a Shorty), you're all set.