In this question we are talking about the element with the largest atomic number in group 1. This is the one furthest down the group.
Statement 1 is correct because reactivity with water increases down group 1. Hence, it has the most vigorous reaction with cold water, as compared to
Statement 2 is correct. All elements in group 1 have one electron in their highest occupied energy level.
Statement 3 is correct. Oxidation is loss of electrons. The element furthest down group 1 will have the largest atomic radius out of the other group 1 elements. The larger the atomic radius an element has, the more readily it can lose electrons, hence the more readily it can be oxidized.