páirtí is a transliteration of the English word "party" in the sense of "a political party - páirtí polaitaíochta, or person/group that is "a party" in a legal sense: "an interested party" - páirtí leasmhar.
cóisir is the Irish word for a celebration, what is called "a party" in English, even though the word "party" means something else.
No, the hints do not say "Is the party tonight".
The hints for the individual words may be "is", "the", "party" and "tonight", but the word order in Irish isn't the same as it is in English, so you can't put the hints together in the same order. The basic structure of an Irish sentences is verb-subject-object, whereas English uses subject-verb-object.