Unfortunately, the teacher knows little about Vishnitz, otherwise, she would not have asked you to write who the current Rebbe is.
Chassiduyot have two manners of continuing their dynasty. One is that there is always only one Rebbe, and that position is passed from father to son or closest relative. This is typical of Belz, Lubavitch, Gur (Ger), and others.
The second is for every son to take on the name of a town (not always the town they live in, and not always a European town) and start their own Rebbeship. This system is typical of Vishnitz, Nadvorna, and many others, especially the tree of the Rachmastrivka and Rozhin dynasties.
There are now two primary Vishnitz Rebbes in Israel, both in Bnei Brak, brothers Yisrael, and Mendel. The Vishnitz Rebbe in Monsey pased away a year or two ago, and he had seven or so sons, each of whom is now a Vishnitz Rebbe (Monsey, Yerushalayim, Boro Park, Bet Shemesh, Kiamesha Lake and a few others).
There is also a branch called Seret Visnitz, a branch called Shotz-Vishnitz, and others
I suggest opening up Wikipedia in Hebrew and writing in ויז’ניץ, that will give you all the information you are looking for, including philosophy, tefillot, learning, history, etc….
Hatzlachah.
If it interests you, the Vishnitzer Rebbe of Bet Shemesh was hospitalized yesterday with Coronavirus.