You're right, the correct legal jargon is "pursuant to" or "in accordance with" (rather than "according to", which is correct content-wise but not the proper lingo).

§ stands for Paragraph, the German term for section (of a statute). This scriggle is not used in NZ legal writing or statutes (nor is it in the UK), but is in fact used by the legal community in the US. With regard to a run-of-the-mill act/statute, I wouldn't use "article" as a translation for Paragraph, article is reserved for higher ranking pieces of legislation.

Finally, Halbsatz is - nomen est omen - one half of the sentence. For easy reference, lawyers like to quote their sources with a high degree of precision, down to the individual part of the sentence. I've seen this translated as "first-half sentence", but only in EU documents - so it's probably not very idiomatic.

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Note added at 18 mins (2003-12-09 06:55:17 GMT)
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Nope, Satz is definitely not clause (clause is a section in a contract and a good translation if you come across § indicating a contractual provision). A German statutory provision is structured as follows:

Paragraph (§) = Section (s.)
Absatz (Abs.) = paragraph (para. or number in brackets)
Satz = sentence
Nummer (Nr.) = number (No.)
Litera = lit.