No and no. Estonians speak a Baltic language, making it most similar to Lithuanian and Latvian, which in turn, makes it somewhat similar to Sanskrit. I am not a linguist, however.
Unless Estonian has been reclassified as a hybrid Balto-Germanic (Scandanavian)—I don’t know.
Estonian is a Finno-Ugric language closely related to Finnish, and distantly related to Hungarian.
I’m not a linguist either but I am Estonian.