Not to the best of my knowledge.
The main Israeli parties are Likud and Labour – mostly secular. Then there are the religious parties (UTJ is the big Ashkenazi party and Shas the big Sephardi party). The next biggest parties are probably Shinui (a center-right party that is devoted to secularism), the Arab parties, Yahad, a newer left wing party, and many other smaller parties. I’ll discuss what I know (which may be wrong, I’m an avid follower but by no means an expert or an Israeli) about the parties currently represented in the Knesset.
http://en.wikipedia.org/wiki/List_of_political_parties_in_Israel
Likud is strongly divided over the Palestinian issue. Ariel Sharon’s policies are pretty well known by now – pragmatic, reluctant withdrawal from at least Gaza. Much of the party does not support this and remains very pro-settler. The language that is used most often is about the lack of a Palestinian partner for peace negotiations – i.e. nobody in the Palestinian leadership is strong enough to disarm and keep a cease-fire, so there is no use in negotiating. This is somewhat of a delaying tactic and I don’t think that there are many members of Likud supporting outright transfer or outright withdrawal – their policy remains pretty murky. As does Sharon, beyond Gaza withdrawal, to which he seems very committed.
Labour is the left wing party. It too is somewhat in disarray. Mostly, Labour supports negotiations but they too have set no firm withdrawal plan. The most commonly held view, IMHO, is withdrawal to the separation fence with dismantling settlements beyond it and annexation of everything else. This is not entirely popular outside of Israel, obviously.
Once you step away from the major parties, which try to build reasonable consensus, you get to smaller parties which can take more niche views. Since Israel is a parliamentary system, you only vote by party, and since coalition building is necessary for forming a government, you don’t feel like you are wasting a vote this way. So Shas represents the needs of the Sephardim and goes after money for their schools, etc, but often forms coalitions with either Labour or Likud. Parties like Shas, who are not directly focused on the Israeli/Palestinian conflict, have shifted their views on a final settlement based on whose government they are in.
Other parties, like Yahad (made up of two old left-wing parties IIRC), are directly for withdrawal to pre-1967 borders with a peace treaty and a two-state solution. The aforementioned, banned Kach party is for transfer, as is the National Union coalition (includes the old party of Moledet, which means homeland, i.e. a homeland for the Jews and nobody else.)
So to answer your questions directly:
- Yes, the Yahad party is for a two-state solution in every sense of the word.
- Yes, the Moledet party, now part of the National Union, was specifically founded for transfer of the Palestinians out of the territories.
- Probably the Israeli Arab parties (which get full representation in the Knesset) are for full citizenship for all Palestinians but to my knowledge no non-Arab party would advocate that as it would be immensely unpopular among the Jewish population of Israel, who would soon be a minority. A little research shows that indeed, Balad, an Arab party does advocate exactly this.
I can’t give a zeitgeist of the average Israeli, but I think the answer would be that there is no average Israeli. Israel is very polarized right now: Arab versus Jew, secular versus religious, left versus right. Each has a party. I would say that among secular Israelis, even ones that used to consider themselves very Zionist (like much of Likud), the settlements and especially the Gaza settlements and the new West Bank settlements, are increasingly seen as security liabilities. IMHO, most Israelis would like the ability to lock down the country behind a security fence and let the Palestinians stew. If a country emerges, great. If they want to be friends, even better.
Religious and right-leaning Israelis (maybe like Zehava) still believe in the right of settlement, and they have many justifications, some of them which actually are pretty good, which they will gladly argue with you. These include God’s word, but also things like Arab underusage of the land, to the victors go the spoils, etc. I’m sure others can do a more capable job than I can in explaining these.
Whew. I hope I haven’t butchered things too badly.