1. In general, for two wavefunctions, we do not have $\langle\psi_1|\psi_2\rangle=0$. Consider for instance two Gaussian orbitals that are identical except for being displaced with respect to each other.
2. The sign of the hopping determines which molecular orbital has the lowest energy
2. The sign of the hopping does not influence the spatial form of the eigenstates, nor does it change the eigenenergies
3. The size of $H$ increases with the number of atoms.
4. The size of $H$ increases with the number of orbitals.
