Greeting the Prima of our pop music

As far as I understand he original text refers to Алла Пугачева. Then I would say "Russia's" or "Russian". "National pop music" souns lame in English.
As for "pop diva" or "pop star", there can be a lot of them, so you'll have to add something like "biggest" or "greatest" to show that she's the #1 among all of them :o)

Sounds right to me:
"congratulated Russian stage Prima Donna/diva on her new home/flat"
or, if you want to keep the word order:
"congratulated Prima Donna of the Russian stage on her new home/flat"

I'd stay away from 'pop' — sometimes эстрада is not what I would call pop at all, (especially if you're talking about Pugacheva...)
'Prima Donna' seems fine to me, despite the potential negative association with the term.

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Note added at 1 hr (2008-08-18 08:59:15 GMT)
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I agree with Mikhail that 'stage' is a bit too generic. However, by using Prima Donna, (or Diva) I think it's pretty clear she's primarily a singer — yet doesn't limit her to singing alone, which none of us would *ever* want to suggest. ;)

Another note:
A Google search for "поздравляла Примадонну отечественной эстрады с новосельем"
gives only one result in which there is no mention of Alla at all!
(http://www.utro.ru/articles/2007/12/11/701031.shtml)

How about:
"congratulated Russian stage prima donna, Alla Pugacheva, on her new home"?

Речь ведь о Пугачевой?
Она такая одна!

This album features music from Russia’s first lady of song, Alla Pugacheva

www.passiondiscs.co.uk/rusin.htm

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Note added at 1 дн38 мин (2008-08-19 08:09:09 GMT)
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http://dictionary.reference.com/browse/scene queen