1) Basically , you're right.
The inquisition didn't look for the jews, since being a jewish in Spain was practically illegal. In 1492 the jews in Spain were given the option of becoming baptized Christians, or leaving Spain. While the Inquisition had no authority over practicing Jews (who could not be branded as Christian heretics), the Inquisition had great authority over the "conversos", many of whom continued to worship as Jews in secret.
In addition , the Inquisition drew up an elaborate list of "signs" by which a "Judaizer" (a relapsed Jew) could be discovered.
So eventually they did chase jews.
2) Indeed , no individual in the Jewish community thought of saving the landless nation. The community itself was trying to survive and keep its tradition. The fact that they had no country just made this mission harder.