yes it is a Jewish surname
No, but a Jewish person can have any surname.
There is no surname that is used only by Jews. There are many surnames that are used both by Jews and non-Jews. Therefore, any surname that is used by a Jewish family is Jewish, and any surname that is used by a non-Jewish family is not Jewish. So any surname can be both Jewish and non-Jewish at the same time.
There are almost no surnames that are uniquely Jewish. If an surname is or was used by a Jewish family, then it is Jewish. If the same surname is or was used by a non-Jewish family, then it is not Jewish. And both can be true at the same time. For example, Cohen is an Irish Catholic surname with no connection to Judaism, yet Cohen is also a Jewish surname related to claims of descent from the Jewish priesthood.
no
The surname Waxman is of Jewish origin, specifically Ashkenazi Jewish. It is a common surname among Jewish communities.
Not in its origin, but a Jewish person can have any surname.
Fanny Tarnow was born in 1779.
Fanny Tarnow died in 1862.
Rudolf Tarnow died in 1933.
Arthur Tarnow was born in 1942.
The name Lewis is a surname for some Jewish families but it is also a surname for some non-Jewish families.