Yes all those families still exist.

Ironically out of the major clans, Tokugawa is probably one of the ones with the smallest number, because during the Edo era only the Shogun and the Kii, Owari, and Mito daimyōs were allowed to use the Tokugawa name.

Yes, though I don't know about Takeda; maybe a branch line survived into the Meiji period. After the Meiji Restoration, the new government abolished daimyo clans but later absorbed the former daimyo into a new modern European-style peerage. So the Date lord became "Count Date". The modern Japanese nobility was abolished in 1947 under Japan's postwar constitution. But descendants of the peerage families or "kazoku," who include former kuge and peers of merit, continue to hold lots of social prestige today. Until recently, most of the emperor's relatives married exclusively into kazoku families.