the process by which a protein channel allows molecules to cross the cell membrane is called?

Answer 1

facilitated diffusion through channel protein

Answer 2

It depends upon whether the molecule is moving with or against its concentration gradient. If the molecule is traveling down its concentration gradient (from areas of high to low concentrations), this would be facilitated diffusion. If against the concentration gradient (moving from low concentration to high concentration), this would require the input of energy--active transport.