Questions & Answers about Wir feiern Mias Geburtstag.
Why is there no apostrophe in Mias?
In English, you write "Mia's", but in German, the possession "s" is attached directly to the name without an apostrophe. You only use an apostrophe in German if a name already ends in an s-sound (like Max or Lukas).
Why isn't there an article like den before Geburtstag?
Geburtstag is the direct object here (accusative case), so you might expect the masculine article den. However, the possessive name (Mias) takes the place of the article. You don't need both!
How is the long word Geburtstag formed?
It is a compound noun made of die Geburt (the birth) and der Tag (the day), joined together by an extra linking "s". Because the last word is der Tag, the whole word is masculine (der Geburtstag).
Why does the verb feiern end in -en here?
feiern means "to celebrate" or "to party". Because the subject is wir (we), the verb takes the standard -en ending, which makes it look identical to the dictionary form of the verb.