Well, you have to decide if these four statements are true or false. Since the statements are in plain English, not understanding them presents a problem. I am not sure I can help since all I can do is use the same English.I'm not sure what they're asking

This is false. Indeed, suppose that such y exists. Then x + y = 1 for all integer x, in particular, for x = 0 and x = 1. So, 0 + y = 1, from where y = 1. But then 1 + y = 1 is false since 1 + 1 = 2.(ii) There exists y in the Integers such that for each x in the Integers, x+y=1

This is true. Given any x, take y = 1.(iii) For each x in the Integers there exists y in the Integers such that xy=x

Mathematics uses the same words and their meanings as regular language. The phrases "for all" and "there exists" don't cease to mean what they usually mean just because they are used to speak about numbers.