OK - my view of things:

- you are now married to a German citizen. Therefore, the EU Directive 2004/38 applies. You have the automatic right to stay in England (and work) as long as your husband does (provided he is a qualifying person, i.e. normally works, or has permanent residence because he has been in the UK for more than 5 years).
- the only (realistic) reason why this may not be true is if the UK authorities consider your marriage to be a marriage of convenience. (The other much less realistic reason would be that you are an obvious threat to society or that you have one of a very small number of very nasty epidemic diseases. ;-))
- the fact that your Fiance visa expires has no influence on this status. You do not need to leave the country. You also certainly don't have to wait for the residence card to be issued.
- You should apply for EEA2 and your husband can apply for EEA1. From what people report here, joint applications are dealt with much faster than EEA2 applications.
- If you leave the country, it might be tricky to re-enter without the necessary documentation, but since South Africans are not visa nationals, this is likely to be a smaller problem than otherwise. The official UK view is that you need a Family Permit (which is free and should be issued very quickly) as long as you have not been issued a residence card. In reality, you should be let in even without a permit - but an overzealous immigration officer might feel like questioning you over this.

As always, it's worth double-checking this information. I am not a immigration specialist. ;-)

Sebastian