You must be knowing that it is very difficult to identify the fossils from their photographs, but the following are just hint and it needs very to verify them.
I am not sure, but the first photo shows affinity to fossil Arctica and the second one is very close to pycnodonte pulaskiensis.
I can't understand what did you want to say about the first picture?
But the 2nd picture is not of pyconodont. Pyconodont is a kind of oyster. But this specimen is sure not an oyster. In this specimen ventral margin is smooth. In the external surface concentric ornamentation is clearly seen.
These fossils are collected from the early Paleocene rocks of South India. The collection area is approximately 150km. away from the present day coastline.
I don't think it is possible to identify these bivalves with any certainty, if the internal features are unknown. The external shape of neither resembles that of Arctica or Pycnodonte (or indeed any oyster). The upper specimen is in its shape similar to Polymesoda, but this shape is not unique. If correct, you would expect the environment to be brackish, or at least near-coastal marine with influx of lagoonal/ deltaic species. If at all possible, collect specimens showing the inside features..
The rock containing these fossils deposited in an estuarine environment. It is also evident from the presence of Physa (a freshwater gastropod) along with typical marine gastropods like Turritella.
The general shape and ornament look somewhat like a Callista in the Veneridae, but the picture of the hinge area is too dark and not zoomed in enough to tell any details. The interior characters are the most important. Is the original shell structure completely gone, or is it possible to carefully open the shell up to indicate interior features?