The state exists - de facto. With US backing, of course it is a "full member" of the UN. Only 3 of 22 Arab League members have normal diplomatic relations with it. The UN does not recognise the illegally obtained territory though. Personally I consider, as I have said, that the state came into being illegitimately.
You are certainly naive and ill-informed. As a full member of the UN Israel is not a de facto state as it has diplomatic ties with 163 countries, perhaps you should look up the definition of the phrase? In fact your definition would state the following countries do not exist (which they most certainly do in all independent sovereignty):
Cyprus
Czech Republic
Liechtenstein
Democratic People's Republic of Korea
Republic of Korea
People's Republic of China
Republic of China (Taiwan)
Slovakia
Iraq, Lebanon, Saudi Arabia, Syria, Yemen, Libya, Sudan, Morocco, Tunisia, Kuwait, Algeria, UAE, Bahrain, Oman, Somalia, Djibouti, Comoros, Eritrea
The Arab states refusal to accept the situation is only fuelling the problem. The majority of the world accepts the legitimacy of Israel, as long as people with your attitude exist there will always be conflict.
Israel does not recognise the West Bank and Gaza as being part of Israel either, but you know that considering your enfranchisement comments.
Israel has NEVER seriously taken any lasting steps to bring about peace. I do not think they want it. Israel are just as guilty of murdering the innocent.
Israel and Fatah were in discussions, especially with finally establishing of Palestinian Authority to enable the handover of the West Bank and Gaza Strip. Hamas rejected all negotiations.
Israel is not de facto state. Israel was mandated legally by the UN, your failure to accept that is a failure to recognise the UN - another problem in itself. Negotiations were taking place before Hamas chose to no longer recognise Israel. Palestine is completely unreasonable to Israeli offers refusing to negotiate.
You are blind to the point of it being frustrating by ignoring absolute fact.