Answer
No. Yes.
Work Step by Step
The sign/direction of the battery’s emf does not depend on the direction of the current flow through the battery. When you apply the loop rule, you add the battery’s emf if you choose a path that goes through the battery from the negative terminal to the positive one. You subtract the battery’s emf if you choose a path that goes through the battery from the positive terminal to the negative one.
However, the terminal voltage does depend on the direction of the current through the battery.
If current flows out of the battery from the positive terminal, and enters the battery at the negative terminal, there is a voltage drop across the internal resistance. The terminal voltage is smaller than the emf.
On the other hand, if current flows into the battery via the positive terminal, and leaves the battery at the negative terminal, as might happen when the battery is being charged, the terminal voltage is higher than the emf.
