As there seems to be a sizeable Palestinian population in the country of Israel…
Do they have the right to vote? Does one have to be Jewish, or living in certain neighborhoods to vote?
If they do, how come they haven’t gotten behind a politician sympathetic to their cause, or is it even possible for a non-Jewish person to lead the country?
Even if its too far-fetched to imagine a Palestinian as Prime Minister, could they form a sizeable minority bloc in their legislative branch?
All Israelis have the right to vote; it is not necessary to be Jewish. There are Israeli Arabs, they do vote and IIRC there is at least one party represented in the Knesset whose voters, member and representatives are predominantly Arabs.
However Arabs from the West Bank, the Gaza Strip or other areas under Isreali occupation but not part of Israel proper are not Israelis, and do not have the right to vote (even, I believe, if they become resident in Israel proper). The population of Israeli Arabs with voting rights is small.
I assume, but I do not know, that Israelis who live in the occupied territories (i.e. outside Israel proper) do have the right to vote in Israeli elections.