I am an Indian national with a German work visa, working for a berlin-based startup company that has a collaboration with a company in Prague. They would like me to work in Prague for a period of 8 months. As I am still working on behalf of the berlin-based company can anyone let me know if it's allowed to work and live in Prague with my German visa?
No, a German visa is a national visa and only gives you the right to work (with some limitations depending on the kind of visa) in Germany, not in any other EU country.
A national visa of a Schengen country usually allows you to stay up to 90 days in a 180 day period in another Schengen country for business/tourism purposes, so even using this right it would not cover a full 8 month stay. And this is not the same as working in another EU country.
You should probably consult with the Czech Embassy on what kind of visa would be appropriate for this case.