Do I need a visa if I'm traveling from Cape Verde?
No, as per TIMATIC (documents database used by airlines), but it is limited to 30 days instead of the regular 90 days. But you can extend it up to 90 days.
Are there any specific documents or vaccinations needed for entry?
You will need to fill the Traveller Declaration
Passengers must complete the “South African Traveller Declaration" before departure or upon arrival at https://www.sars.gov.za/travellerdeclaration/ .
What is the process for extending a tourist visa if needed?
You are to apply online (source)
Extending the validity of a temporary residence permit or applying for change of status or conditions
An application for the extension of the validity of a temporary residence visa must be done at least 60 days prior to the expiry of the visa by submitting an application online at www.vfsglobal.com/dha/southafrica. There is a fee payable when applying for an extension of the validity of a temporary residence visa.