I am a dutch guy who is study/work's in the uk, I am going to marry a
South African in the Uk.  Can she work after we are married and does
she get a permanent residency permit. How long does she have to wait
to get a passport from the eu?

I think that in the first place it will depend on whether you have UK
permanent residency, ie indefinite leave to remain in the UK. If so,
after your marriage, your SA wife should also be granted this status,
and - subject to conditions (including your remaining married) - after
5 years would be able to apply for UK citizenship and passport. (See
http://www.ukimmigration.com/family/uk_spouse_visa.htm  )

I have no idea what rules apply in the Netherlands; and it is possible
that it would be easier for her to apply for Dutch citizenship and
passport on the basis of being your wife, than for UK citizenship.
(You use the term "passport from the EU", but the EU as such does not
issue passports, only individual EU countries.)

assuming that you hold a valid passport for the eec then once you are
married and your wife has a valid spouse or finance visa  national
insurance number she can work immediately. After a year she can apply
for permanent residence. After five years she can apply for a britsih
passport, unless you yourself become a
british citizen in which case it is three years. However note that she
cannt leave the uk for more than 90 days in a year during this period
and if when she applies for a pasport five years prior she was out of
the uk they will refuse it and you will have to apply again.