I think the "answer to q2" here (https://mathoverflow.net/questions/199097/which-unfoldings-of-the-hypercube-tile-3-space-how-to-check-for-isometric-space/39282

I think the "answer to q2" here (https://mathoverflow.net/questions/199097/which-unfoldings-of-the-hypercube-tile-3-space-how-to-check-for-isometric-space/392828#392828 https://mathoverflow.net/questions/199097/which-unfoldings-o...) is what you want!