Learn Icelandic: Hvenær er brúðkaupsafmælið þitt?

It is a compound word made of brúðkaup (wedding) and afmæli (anniversary/birthday). The -s- in the middle connects them together, and the -ð at the very end is the definite article meaning "the".

Why does it say "the wedding anniversary your" (brúðkaupsafmælið þitt) instead of just "your wedding anniversary"?

In Icelandic, the most natural way to show possession is to put the possessive word (like þitt) after the noun. When you do this, the noun must have the definite article attached to it (the -ð ending). So, "the anniversary your" is the standard way to say "your anniversary".

Why is the word for "your" þitt instead of þinn or þín?

Because afmæli is a neuter noun. Possessive words have to match the gender of the noun they describe, so we must use the neuter form þitt.

Since we are learning about time and months, how would I answer this question by saying "in May"?

To answer a hvenær (when) question with a specific month, you use the preposition í. For example, you would answer Það er í maí (It is in May).

Can I use hvenær to ask what time it is right now?