1. No this is a false statement, channel proteins create an opening in the membrane which allows solutes to move down the concentration gradient while carrier proteins create a situation in which the protein can interact with the solute and essentially escort nutrients and ions through the membrane against the gradient. So channel proteins would be considered passive while the carrier proteins would be active transport.
2. This statement is also not entirely correct, because If the membrane is permeable to an ion and Eion is not equal to Em then the ion will cross the membrane pulling Em towards Eion. So if the membrane becomes more permeable to Na+ ions then the influx will increase down the concentration gradient but the potential will decrease not increase.