Perhaps, but it might be easier to find some special superconducting material that has a critical temperature below room temperature and still works at room temperature...let's say because it's super robust against external perturbations. Ultimately it will depend on the mechanism and the...
To your first question, think about the position vectors that constitute the Bravais lattice. Simply repeating those vectors yields the full lattice structure. Well, the wave vectors k are just another way of reproducing the Bravais lattice, only this time in 'momentum space.' The E versus k...