Hello Flavia, I really liked your post, I'll try to help (a little bit).
to organize or hold an event
Let's have a party.
(from Oxford Learner's Dictionary)
I have a party tonight. (1)
(1) Meaning I am organizing the party, or the party is at my place.
Look the following:
Anna's mother is your friend and she is making an invitation (on the phone).
Your friend: "We have a party tonight to commemorate Anna's birthday, would you like to come?"
"I'm so sorry to invite you at such short notice..."
You: "Sure, I'll be there! At your place, right?"...
You (thinking after the phone call): "Oh gosh!, I don't feel like going shopping right now, what should I do? I need to buy a gift."
Flavia, I think you are absolutely right when you wrote your examples.Fatima´s birthday is today.Today is Fatima´s birthday.
That is the usual way to be clear when you talk about one's birthday.
I don't know wheather "collocation" is the term to describe that, but I am quite sure
that's the way they (native speakers) do, I guess
that's the most common structure.
Sorry for being redundant.