From left to right: P. pensylvanica, P. hydropiperoides, P. longiseta, P. punctata, P. glabra, P. lapathifolia.
Second photo, the one on the bottom is H. hydropiperoides (P. pensylvanica is on top).
On beach. At this beach, coastal erosion is eating into a patch of vegetation on the dune, consisting of grass and Smilax bona-nox (the Smilax is all the leaves visible in the grass). At the leading edge, the below-ground parts of the Smilax fall onto the sand. Monograph by Coker 1944 (Journal of the Elisha Mitchell Scientific Society 60) describes structures I've labeled in indoor photos. Coker claims spines on tubers, but these mostly had prickles only on the wiry extensions off underground nodes.
Drawn from life on location. Mistakenly wrote "flower heads" instead of "flowers." :[