If it is possible, suggest me a protocol, or suggest me a researcher or lab where this kind of research is active. Particularly, the main interest is cell division rate and cell morphology change study under different climatic situations.
Change in cell density (cell number) in time, will show the division rate. Any microscope and camera system that can show the cell features you want to image, would be good enough. The hard part is getting the actual cell division all the way through the process.
We work with fungal spores pretty much same size as micro-algae. We develop the oCelloScope live-cell imaging platform which is used to image in time-lapse and get fast growth kinetics and morphology. We mainly work with bacteria and fungi but I cannot see why micro-algae should be different. I have tried with Chlorella and that worked just fine. Get in touch if you want to see what we do.