2. Values of $k$ that differ by an integer multiple of $2\pi/a$ describe the same wave. Therefore, all information is already contained in the 1st Brillouin zone.
3. The LCAO wavefunction is $|\Psi\rangle = \sum_n\phi_n|n\rangle$. The Schroedinger equation yields $\varepsilon \phi_n = \varepsilon_0 \phi_n - t \phi_{n+1} - t \phi_{n-1}$. Plugging in the Ansatz $\phi_n = \phi_0 e^{ikna}$ yields
3. The LCAO wavefunction is $|\Psi\rangle = \sum_n\phi_n|n\rangle$. The Schrödinger equation yields $\varepsilon \phi_n = \varepsilon_0 \phi_n - t \phi_{n+1} - t \phi_{n-1}$. Plugging in the Ansatz $\phi_n = \phi_0 e^{ikna}$ yields
