The Plant referred to is very likely Dicksonia Antarctica, a species of evergreen tree fern native to eastern Australia, ranging from south-east Queensland, coastal New South Wales and Victoria to Tasmania. These are not related to Cycads at all. Interestingly this species was planted here at Kirstenbosch and has actually become a problem. They have now invaded the natural indigenous forest around Kirstenbosh. Our own indigenous Cyathea species are very similar and point to the time when South Africa and Australia were once connected in the old continent of Gondwana.
The spider in the first picture is the Black legged golden orbweb spider (Nephila fenestrata) which only as recently as 2002 has crossed over the formidable mountain barrier to the east of Cape Town and can now be seen on the Peninsula. They make huge orb webs and interestingly the females are large, measuring 15 - 40 mm in length, with a leg span of 100 - 120 mm, while the male is only about 5 - 9 mm, with leg span of up to 25 mm, and it is only about one thousandth of the female's weight. They can inflict a nasty bite!