As for why Israel uses more water than Palestine, the answer is that Israel had invested in building an economy. Most water is used for agricultural and industrial uses. The Palestinians by contrast invested in war, digging up their water system to make qassam rockets out of their water pipes, and have no meaningful industry.
The reality is that Israel uses less water per dollar of GDP, and you are double counting water. Israel reuses household water for agriculture, so you are counting one litre twice when it is first used as drinking water and then used again for agriculture.
The Palestinians, including the Jordanians, having not focused on advances like that, use a litre only once either for drinking or for agriculture.
If you ever go to the middle east, visit Jordan and then Israel. Notice that Jordan is a barren desert, while Israel is lush with farms. Realize that this is because Israel makes efficient use of water while Jordan does not, even though they have essentially the same resources.
I point out Jordan because Jordan is an independent Palestinian state and shows what the Palestinians are not capable of even when not occupied and given ample opportunity and resources.