Um, no, no, no and no.
As far as my understanding of the NHRA, the act is fairly comprehensive. As far as shipwrecks go - "wrecks, being any vessel or aircraft, or any part thereof, which was
wrecked in South Africa, whether on land, in the internal waters, the
territorial waters or in the maritime culture zone of the Republic, as
defined respectively in sections 3, 4 and 6 of the Maritime Zones Act,
1994 (Act No. 15 of 1994), and any cargo, debris or artefacts found or
associated therewith, which is older than 60 years or which SAHRA
considers to be worthy of conservation; ..."
are protected. So if the wreck is less than 60 years old, feel free to pick up something (although you still need a salvage permit to legally remove stuff from a wreck). The act also does not just refer to the wreck itself, but includes the cargo, so anything "picked-up on the beach" should be turned into the nearest museum. I've salvaged wrecks in the past, but always with either a salvage permit, or under the governance of a museum.
As far as fossils go, ...
"No person may, without a permit issued by the responsible heritage resources
authority—
(a) destroy, damage, excavate, alter, deface or otherwise disturb any archaeological or palaeontological site or any meteorite;
(b) destroy, damage, excavate, remove from its original position, collect or own
any archaeological or palaeontological material or object or any meteorite;
(c) trade in, sell for private gain, export or attempt to export from the Republic
any category of archaeological or palaeontological material or object, or any
meteorite; or
(d) bring onto or use at an archaeological or palaeontological site any excavation
equipment or any equipment which assist in the detection or recovery of
metals or archaeological and palaeontological material or objects, or use such
equipment for the recovery of meteorites."
So megalodon teeth are technically also a no-no.
So in summation - NO