What does "Have" mean in these sentences?

Have => drink/eat. It’s casual English.

“She was the girl to have had a cup of tea” is a very strange sentence; I recommend you ignore it. It’s closest to your second guess to the meaning, but your second guess is better English than the sentence yuo want us to explain! It’s shorter and uses a more appropriate structure.

> He had a cup of coffee and a pastry for breakfast.

Is first sentence correct? What does it indicate?. Action happened?.
She was the girl to have a cup of tea.

Yes. The second one is very strange. I ignored that.

“She was the girl to have a cup of tea” seems to almost indicate habitual action, as in “she was the girl who would usually have (order/drink) a cup of tea”—that seems to be equivalent to the first sentence you posted.

I feel like I’m reading the scene in The Hobbit, where Bilbo says good morning to Gandalf, and Gandalf questions which of seven or eight ways Bilbo means it, lol! I took the above statement the following way…the girl is being described as someone who would normally have a cup of tea, as in “He was the type who would buy a cup of coffee in 85 degree weather.”

She was the girl who liked her cup of tea—she was the right girl to give a cup of tea to [pardon the end preposition]. You pegged her, she likes a cuppa.

“Have” indicates ownership. If you want to show volition or habit, you need to add a qualifier.

She loves to have (or having) a cup of tea every day.

She has a cup of tea every day. (That tells you nothing about whether the girl enjoys it.)

She has a cup of tea in her hands (so can’t pick up the pencil you just dropped.)

Your examples make no sense in idiomatic English (which, I know, is confusing)

If you mean “want,” why not just use that?

She wants a cup of tea each morning.

She wanted her tea yesterday morning but was too busy.

In addition to all the above examples, it could well mean
“She was the girl, who was (going) to have a cup of tea.”

but it’s impossible to tell out of context. the probable meaning depends not only upon the surrounding text and situation, but also the age of the text.

Many of these possible meanings represent styles of usage, which are no longer common.

What is indisputable is the fact that, in this case, the word “have” means “consume”, and such usage is common in casual speech, as @the100thmonkey said

When I read this, I was immediately drawn more to the beginning of the sentence “She was the girl…” than to the “to have a cup of tea” segment. My interpretation of this sentence is more of: She was the (one) to (be granted) a cup of tea as if she had been chosen to win, or be granted, a cup of tea. It brings to mind an English countryside, a manor filled with orphans, and some stuffed shirt has chosen one of the young ladies to join the gentry for tea.
Which means, the second sentence “She was the girl to have had a tea” is different. If you notice- there’s no cuppa there, only ‘a tea.’ The connotation’s different. It’s more abrupt without ‘a cup of,’ which makes me feel like the sentence is more final, more close-ended, like “She was the (one) to (at one time possessed/consumed/took/pilfered/etc) a tea.
I agree with gailcalled- it’s hard to say what it means, fully, without the surrounding context.

It is not a sentence that would be commonly used in American English. I agree it could mean she was the girl meant or intended to have a cup of tea. Or, it could be she was supposed to, or going to, or intended to have a cup of tea. You need more context to understand. Ight even need further explanation by the author. We are just guessing, it isn’t clear.

How about inserting She was the type of girl to have a cup of tea? As opposed to a coffee drinker? It isn’t, as others have said, clear.

That sentence had had a had in it but I had to change had to have to have a proper sentence.