I am positive that the GPU will fit into the motherboard, but I am not positive that it will fit in the case. I could be wrong, as I am just judging from the pictures on Newegg. The reason I'm doing that is because after a quick Google search for the GPU clearance, I found nothing. I think it will fit in the case, but I am not positive.
Yes, all will fit and play nice together. The small case has a wide open area for the 9.2" long gfx card. I just happened to have built a budget gamer with that case for someone not long ago. I presume you have a sufficient size PSU for the card?
Rosewill makes some decent PSUs, but the one in that case doesn't look like a very good one. The R9-270 is a 150W card. That would require a very substantial 450W PSU. The one that comes with the case doesn't look to be one.