I agree with most of everything you wrote above, but I can't really recall a situation in which the settlers attacked and tried to kill an innocent bystander that they had no reason to suspect.
(While in the times of the second intifada, a lot of suicide bombers infiltrated into settlements and murdered pepole over there).

As an Israeli myself, I agree that we should let go of the settlements, but more due to international pressure and the fact that protecting them requires a lot of resources that could be spent on other things, like populating the southern regions of Israel.

However, I really don't think that it will help negotiations with Palestinians in the slightest, I want to ignore Hamas (who put the destruction of Israel as one of the main focuses of the organization), because even when it comes to Mahmud Abas, he refuses to acknolwedge Israel's right to exist, especially as a jewish state.
As long as this thought process rules the Palestinian leaders, I really don't think that the Israeli government should do anything that harms the well-being of it's citizens...

Well, it wasnt being applied to any palestinians, actually.  To my understanding (of jerusalem and the wording of the article) these were all arab-israelis.  So its just a reference to the israelis that participated in this crime, from the young child to the old man.  They seem more akin to a pack of rabid dogs, to be honest.  And people dont typically wait for a rabid dog to kill someone/something before they deal with it.

Palestinian doesn't just mean person who lives in the land governed by the PA, it refers to a people.

A people who weren't seen to exist as a distinct national and ethnic group until Israel was founded. Funny, that. It's almost as if something dishonest were going on.

Well having a country established right on top of you probably does build up a national identity pretty fast.

Needing an excuse to demonise said country also helps to speed up the identity building process, I've heard. As does not being allowed to live in any other Arab state.

I'm sure that the situation could have been dealt with much more easily if Egypt and Syria, two real countries, had offered to take care of the Arabs in Palestine, but that might have made it harder to justify bombing Israel. We couldn't have that, could we?

You can't really just ignore Hamas as long as they are the democratically elected government of Palestine.  Even if the PLO wanted too they couldn't enforce a deal on the West Bank, and they're too foolish to make seperate deals.

The world is trying too by not recognizing them, but it's not tenable and if anything only boosts their popularity.

Of course recognizing them also means making the west bank responsible for anything they do.  Which would be sad, but would also lower their popularity... because right now they can play it both ways, build improvements and help people and attack without penalty, outside of Israel strikes which they don't care about because it only helps their cause and they don't actually give a shit about the people of Palestine.

if the republicans in a quarter of the states kill all the democrats, they should be recognised as a legitimate elected government?

You can't really just ignore Hamas as long as they are the democratically elected government of Palestine.  Even if the PLO wanted too they couldn't enforce a deal on the West Bank, and they're too foolish to make seperate deals.

The world is trying too by not recognizing them, but it's not tenable and if anything only boosts their popularity.

Of course recognizing them also means making the west bank responsible for anything they do.  Which would be sad, but would also lower their popularity... because right now they can play it both ways, build improvements and help people and attack without penalty, outside of Israel strikes which they don't care about because it only helps their cause and they don't actually give a shit about the people of Palestine.

Actually it seems (and I didn't expect it either) that ignoring Hamas is working in a way. The people of Gaza know that Hamas is in charge and are starting to blame them for the fact that they are worse off than the people in the West Bank. From what I've read (and to be honest the information was sketchy at best) Hamas is much less popular now than they were when elected.