Yes, the northern kingdom consisted of those who are the lost 10 tribes. Wikipedia has the following on Mordecai's genealogy:
Genealogy

The tablet of Mordechai's ancestry in the tomb traditionally ascribed to him and Esther
The
Targum Sheni gives his genealogy in more detail, as follows:<a href="
Mordecai - Wikipedia"><span>[</span>b<span>]</span></a> "Mordecai, son of Jair, son of Shimei, son of Shemida,<a href="
Mordecai - Wikipedia"><span>[</span>c<span>]</span></a> son of Ba'anah, son of Elah, son of Micah, son of
Mephibosheth, son of
Jonathan, son of Saul, son of
Kish, son of Abiel, son of Zeror, son of
Bechorath, son of Aphiah,<a href="
Mordecai - Wikipedia"><span>[</span>d<span>]</span></a> son of Shecharim,<a href="
Mordecai - Wikipedia"><span>[</span>e<span>]</span></a> son of Uzziah, son of Sason,<a href="
Mordecai - Wikipedia"><span>[</span>f<span>]</span></a> son of Michael, son of Eliel, son of Amihud, son of Shephatiah, son of Penuel,<a href="
Mordecai - Wikipedia"><span>[</span>g<span>]</span></a> son of Petah,<a href="
Mordecai - Wikipedia"><span>[</span>h<span>]</span></a> son of Melokh, son of Yerubaal,<a href="
Mordecai - Wikipedia"><span>[</span>i<span>]</span></a> son of Yeruham, son of Hananiah, son of Zabdi, son of Elpa'al, son of Shimri, son of Zebadiah, son of Rimoth,<a href="
Mordecai - Wikipedia"><span>[</span>j<span>]</span></a> son of Khashum,<a href="
Mordecai - Wikipedia"><span>[</span>k<span>]</span></a> son of Shekhorah, son of Gazza, son of 'Uzza, son of Gera, son of Bela, son of
Benjamin, son of
Jacob the firstborn, whose name is called
Israel."<a href="
Mordecai - Wikipedia"><span>[</span>21<span>]</span></a><a href="
Mordecai - Wikipedia"><span>[</span>22<span>]</span></a> The same genealogy is inscribed on a massive metal tablet in the
Tomb of Esther and Mordechai (pictured).
As to why he called himself a Jew, there could be various reasons. But foremost he seems to have been a Benjaminite.