I wouldn't hesitate to rent a car around Cape Town, although I wouldn't drive outside the city at night. But that would be my attitude in most cities around the world! By driving yourselves you will have a lot more flexibility over where and when to stop, eat, take photos etc. Although I might be tempted to take a tour of the winelands so I could have a few tasters.
You'll have 5 full days in and around Cape Town but it will be winter. The southern right whales will be around and the proteas should be flowering, which attract sunbirds so I would suggest whale watching (from False Bay or around Hermanus / Walker Bay) and visiting the Kirstenbosch Gardens as other activities. You'll need some flexibility in your itinerary if you want to go up Table Mountain, and as soon as you have clear morning get up there, because you could easily get 4-5 days of cloud. Driving yourselves, you can visit Kirstenbosch, visit the Constantia area vineyards, Boulders Bay penguin colony, Cape Point (keep an eye out for ostrich, game and baboons) and then back along Chapman's Peak Drive for the sunset as one full day out. You could also do Walker Bay for sharks and whales and Betty's Bay penguins in a day trip. I would definately recommend Robben Island for an introduction to the contemporary history of South Africa and if you want to do a township tour, I have been recommended Laura's by an old colleague of mine who now lives in CT.
Sorry I can't answer your other questions. Enjoy the planning!