First, let me say, happy leap year day! And now, on with it:

Chapter 27:
Is this where "Amen" originates? Does it mean anything in particular?
Ted: I've always heard that "amen" is equivalent to "so be it." This would seem to be confirmed by Numbers 5:22. An online dictionary indicates that the origination of the word is from the Hebrew.

Chapter 28:
What does "you are called by the name of the Lord" mean?
Ted: Essentially, it just means that they were to be the Lord's "elect" people, chosen among all the people of the earth to receive His blessings in the promised land. It means that they were a people holy (set apart) to God, who had chosen them to be His treasured possession (Deuteronomy 14:2). In a sense, His "name" was on them, because they were associated and identified with Him.

28 Doesn't make a lot of sense to me. It talks about God cursing the land so it will not produce, but then goes on to say that their enemies will eat the product of the land. It says that God will kill everyone by turning rain into dust, but then it says everyone will be cursed with illness and oppression and scattered among their enemies.
Ted: It doesn't mean that all of the Israelites, at once, would be adversely affected by any of the plagues or disasters. For instance, the land of one tribe might not produce crops, enemies might overrun another tribe and eat their crops, rain might not fall on another tribe's land, and those in yet another tribe might be cursed with illness and scattered among their enemies.