I see no one so far has commented on the "nonsense" phrase "sim saladim... " (or, in some versions, "sim salabim...").

I had the vague feeling I had encountered this phrase before, or something like it, in another context. (The song didn't ring a bell, apart from this phrase.)

I think I found the answer in a German book:

Lauter böhmische Dörfer: wie die Wörter zu ihrer Bedeutung kamen [Pure Bohemian Villages: How Words Came to Their Meaning] by Christoph Gutknecht (München: Beck, 2003), page 131:

"Simsalabim"

"Bismi llahi l-rahmani l-rahim"—mit dieser arabischen Formel beginnt jede Koransure. Sie bedeutet: 'Im Namen des barmherzigen und gnädigen Gottes!' In islamishen Ländern wird sie als Ausruf in vielen Lebenssituationen benutzt.

Sie fragen, was Bismi llahi l-rahmani l-rahim mit der deutschen Sprache zu tun hat? Die Antwort wird Sie überraschen: Die arabische Formel ist—in abgekürzter, entstellter und ironisierender Form—auch bei uns geläufig. Allerdings in anderem Zusammenhang: als Begleitspruch im entscheidenden Moment bei der Ausführung eines Zauberkunststückes: Simsalabim.

["Simsalabim"

"Bismi llahi l-rahmani l-rahim"— with this Arabic formula begins every Quranic sura. It means: 'In the name of the merciful and gracious God!' In Muslim countries it is used as an exclamation in many life situations.

You ask, what does Bismi llahi l-rahmani l-rahim have do with the German language? The answer may surprise you: The Arabic formula is—in an abbreviated, distorted and ironic form—also familiar to us. However, in another context: as an accompanying slogan at a crucial moment in the performance of a magic trick: Simsalabim.]

So, I infer that, in German, "simsalabim" means something like "abracadabra" or "hocus pocus."

I also found "simsalabim" in several Indonesian books. Now, it makes sense that, since Indonesia is a Muslim country, the Indonesian language would have lots of loan-words from Arabic. Accordingly, whenever "simsalabim" is used in Indonesian, it is usually either italicized or put in quotation marks, as if the writers know they are using a foreign word. And, when I used Google Translate (which is far superior to Babelfish, by the way) to translate from Indonesian to English, "simsalabim" was translated as "voila"! So they translated an Arabic-to-Indonesian loan-word into a French-to-English loan-word! How clever and appropriate!

Here are some other illustrative quotes I found:

Now, we are not talking about sim-salabim sleight of hand or presto/change-o magic here. (US, 1998)

—abracadabra, hocus-pocus, sim salabim, OPEN SESAME!— (UK, 1997)

Jadi, yang mesti ditimbulkan pertama kali adalah kesadaran bersama. Tidak bisa "sim salabim." Setiap elemen bangsa ini harus menyadari kecenderungan perubahan ini. [So, what should be first generated is shared awareness. It cannot be "Voila." Each element of this nation must be aware of this change in trend.] (Indonesia, 1995)

Ia berubah bukan karena sim-salabim tanpa penyebab yang jelas. [He changed not because of sim-salabim, but without obvious cause.] (Indonesia, 1999)

Islam bukanlah agama sim salabim, tetapi Islam adalah ajaran yang memiliki energi dengan merefleksikannya dalam dunia. [Islam is not religion Voila, but Islam is the doctrine of the reflected energy in the world.] (Indonesia, 2000)