The specimen in your microscope field image certainly looks like to be a centric diatom or it could also be a member of the family Chrysophyceae but it requires a higher magnification to shed light on the right direction. However, the species growing on the plate is perhaps a benthic species of microalgae.
The attached image is not informative enough. Please if possible provide some better images with higher magnification. But these suggestions might be true: Cosmarium and Chlorella (please see the attached image).
I think there are diatoms. However, in cultures it is difficult to determine diatom species. Usually the shapes change during the culturing period. The final individuals are not identical with the orginals. Therefore a species determination is not possible any more.
Besides there are Chlorella like green algal cells.