If you're a US citizen - residency rules do not apply to you. US citizen is a tax resident in the US by definition.
So it doesn't matter where in the world you live or earn money, if you're a US citizen - all of your worldwide income is taxed in the US.
If you're self-employed - yes, you still need to pay self employment tax (unless there's a totalization agreement with the country where you pay your social security taxes).
For that matter, the treatment is exactly the same as of any other US-based sole proprietor. The fact that your address is not in the US is of no consequence.
If you own a foreign corporation (and from your question it sounds that you do) - then it is even more complicated, more forms are required and more taxes are to be paid in the US. If you have foreign investments and pension accounts - more forms and more taxes. Beware of PFIC rules biting you.
As to S-Corp - there may be other potential pitfalls there.
Also, don't forget FBAR (form 114) and FATCA (form 8938).
More info on how the US government punishes its citizens abroad can be found here.
I suggest discussing this with a licensed tax adviser (EA/CPA licensed in the US) and also with a tax adviser in your country of residency.