Will. As human beings, created in God's image and likeness, we have the ability to know and to love. Our intellect does the knowing and our will does the loving. Our will is what we use to choose good or evil. Here we ask that God's Will be done - we want to want what God wants.
tuo, tua, tuum, all mean THY - the difference is that they describe masculine, feminine or neuter nouns.
In heaven. Last part we learned in caelis means in heaven. Technically caelis is the plural (heavens) and caelo is singular, but when we're translating the difference is a bit fuzzy.
Our. Noster, nostra and nostrum all mean our - the difference is for describing masculine, feminine and neuter nouns.