Very cute game and the minigolf mechanics felt very smooth!! Sadly, I couldn't get past the cave jumping-puzzle because the camera kept snapping around in the tight space :')
Yes, with mouse. I was moving it, but it was hard to aim properly because sometimes it wouldn't allow me to put the camera right behind the character, because I was standing too close to a wall.
I'd tested it on Firefox and Chrome and it works on both. There's a lot that can go wrong with browser stuff though so who knows what it might actually be