The correct response is that only II is true:
I. If you conduct a significance test you assume that the alternative hypothesis
is true unless the data provide strong evidence against it.
False - in any significance test, you must assume that the null hypothesis is true. After all, when we test for significance, we are concerned with some $\alpha$ value that represents the probability of a Type I error (i.e. rejecting a null hypothesis assuming that it is true). In calculating this probability, we can contextualize the likelihood of our observed data being meaningfully different (as opposed to being a result of chance).
Example - Suppose we are testing the likelihood of our coin being unfair and that we decide to flip it several times and track the proportion of times it lands on heads and the proportion of times it lands on tails.
The null hypothesis may be that the proportion of heads and tails are equal (.5 each).
The alternative hypothesis may be that they are unequal.
Significance testing can allow us to understand the probability that we make the wrong conclusion of the coin being unfair (e.g. because .58 of the outcomes were heads and .42 were tails) given that it's actually a fair coin.
II. The null hypothesis and the alternative hypothesis are always mutually
True - The null hypothesis and alternative hypotheses must be mutually exclusive (i.e. only one of the two can be true) and exhaustive (i.e. collectively represent all possible outcomes).