Ja, zum Beispiel so:
"Why did you book a restaurant for tonight, his birthday is tomorrow!"

Das ist zwar richtig, bedeutet aber eher "er hat doch erst morgen Geburtstag!" (vorwurfsvoll).

Karina möchte wissen, ob man "er hat morgen Geburtstag" (neutral) mit "his birthday is tomorrow" übersetzen kann, und da würde ich sagen, im Prinzip schon, aber "it's his birthday tomorrow" wäre mE idiomatischer.

I wouldn't really say that "his birthday is tomorrow" is by itself negative in any way. In addition to the two options given, another is "tomorrow's/tomorrow is his birthday." For some reason, though, without the contraction it sounds stilted, which means I wouldn't use either in more formal writing or speech. In everyday conversation, I'd have no problems using "tomorrow's his birthday," though.

Meine Antwort sollte unter dem Vorzeichen "Ja, aber nur in bestimmten Situationen" stehen. Tut mir Leid, wenn das nicht klar wurde.

I think this might come under the heading of how to put new information at the end of the sentence in English (starting with a "placeholder" it being one method).

If the information "his birthday" and "tomorrow" are both new, as when someone has just mentioned a a male person (thus "his"), it would be idiomatic to say
"It's his birthday tomorrow."
or when starting a new conversation
"It's John's birthday tomorrow."
If the subject of his birthday is being discussed and "tomorrow" is important new information, you might tend toward
"His birthday is tomorrow."

This is a very interesting point. Basically there are three possibilities:

a) His birthday's tomorrow.
b) Tomorrow's his birthday.
c) It's his birthday tomorrow.

These three first have to be discussed on the assumption of normal (neutral) intonation and stress placement (because by varying those, you can achieve almost any result with any of the versions). The main variable is whether you are thematizing (talking about) 'his birthday' or 'tomorrow'. In (a) you are thematizing his birthday and specifying that it is tomorrow. In (b) you are thematizing tomorrow and noting that it is his birthday. In (c) tomorrow is the still the theme (anticipated by 'it'). So what's the difference between (b) and (c)? In the neutral form, I would say none, but the two sentences allow you to 'mark' the elements in different ways to express further nuances.

I would guard against attributing 'affective' meanings (e.g. reproach) to any of the structures as such. Such meanings are more properly attached to marked stress and intonation (which, it is quite true, are more likely to be linked with one rather than another basic structure).

It might be changed a bit by the pronoun ("his"), which implies that the person concerned has been mentioned.

In (c), I think I would consider the theme to be the person whose birthday it is (he/his), and the rheme to be the calendar item. If the event were not his birthday but his driving test, we might say:

" he's got his driving test tomorrow."

I suppose using a noun rather than a pronoun implies that it is something new, but I think I would tend to regard what is mentioned first as belonging to the class of things we were talking about.

If we were talking about events in John's life I would expect
"His birthday's tomorrow."
If we were talking about the week's events, I would expect
"Tomorrow is John's birthday."

It may not be that clear-cut, of course. I'm thinking out loud, so to speak.

M.E. ist da ein Unterschied zwischen gesprochener und geschriebener Sprache.
Ein Sprecher kann nach Bedarf Betonungen setzen, wo auch immer. Im Werbsprech, der ja zunehmend unsere Sprache beeinflußt, ist es nicht unüblich, den Akzent ans Ende zu legen: 'Buy (or do whatever else) now!'

Es ist im Deutschen ja nicht anders. Die Sätze 'Er hat morgen Geburtstag', 'Sein Geburtstag ist morgen', 'Morgen hat er Geburtstag' etc. sind alle möglich, aber nicht in allen Situationen.

#8 Definitely. I am assuming normal stress and intonation (though "normal" can vary with accent.

#9 Indeed.
Of course each language has different restrictions that affect the ability to move words around - or the methods used to do so.