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No. PDFs only uses the PostScript imaging model, not the PostScript programming language.

Ah, interesting - I always though PDF was just a superset of PostScript, but it looks like you are correct: http://www.adobe.com/print/features/psvspdf/

Yeah, but you won't see a TeX editor very soon.

PDFs generated by Adobe Acrobat have Javascript in them (for forms mostly). You are free to not interpret it though.

You can render PDFs in a Webkit view.