Answer to Question 1
For a semiconductor with an infinite lattice of potential wells, which the Kronig-Penney model assumes, the electron energy levels are no longer discrete but continuous. The model holds to a very good approximation, since even a relatively small order of magnitude of atoms (103) can make the levels nearly continuous.
Answer to Question 2
b.
This statement is not true. Carbon nanotubes have extremely high thermal conductivity, which shows that thermal and electrical conductivity are interconnected. Nanotubes have the ability to carry large currents and also carry away the heat associated with large currents, making the maximum current density they carry large enough to rival the critical current densities of some superconductors.