Based on the way the question is phrased, it seems like we are only rolling a single die one time. Therefore, the probability of a single die showing a 1 and a 4 at the same time is 0.
You are correct about part 2. One way to think of it is the following
P(1 or 4) = (Number of desired outcomes) / (Number of total possible outcomes)
P(1 or 4) = 2 / 6 = 1 / 3