Answer 1
I like to look at it this way. An Italian can move to Germany go through a process and officially become German. Germans who moved to America are still German.
And the same goes for Jews, if you descended from a Jew, you are a Jew. If you convert to Judaism, you are a Jew. Look at the Jewish nationality like a country with the borders being Judaism, rather than physical borders. When you convert you become a "citizen" of this culture. Yes, there is still a "Jewish ethnicity" and a non-Jew can never ethnically become a Jew. Just like an Italian could never ethnically become German. But a non-Jew can become Jewish by nationality.
Answer 2
If you mean without converting, some non-religious Jews might answer yes; you could move to Israel, or live among Jews or simply keep Jewish customs and practices. The religious answer is that you need to convert with a valid conversion, which includes (among other things) the intent to live as a Jew.
Answer 3
No. A person who is born a non-Jew cannot become exclusively a "Jew by nationality." That person needs to become a Jew in the religious sense in order to embrace the nationhood-aspect of Judaism.
Contrary to the analysis provided in Answer 1, while Israel is the Jewish State, Israeli citizens are Israelis, not necessarily Jews. Conversion to Judaism is a religious process, not a citizenship-like process (which exists in Israel for Israeli citizenship).