Could you provide some basis for those claims? I'm not saying your wrong or right, but especially for this situation, we need some reason to believe ...
Generalized bias aside, is the UN similarly biased specifically in officially classifying Israel as a (colonial) occupying force and the Palestinian population as refugee?
The UN is blatantly biased. There are ~50 Islamic states in the UN that compulsively always vote against Israel. These Islamic states have even made rambling and screaming about Israel a mandatory ceremony (Item 7) at UNHRC sessions.
I'm not going to defend Israel's actions of the last weeks, but
Israel cannot be called a colonizer. That's stretching the meaning of the word too far, only for demagogic effect.
And yes, the UN are biased. The number of resolutions against Israel is absurd. From wikipedia: "Since the UNHRC's creation in 2006, it has resolved almost as many resolutions condemning Israel alone than on issues for the rest of the world combined." I don't think any Israeli loses sleep over UN resolutions, nor does it give any Palestinian hope.
Hamas cannot win the conflict with Israel, at least not in the foreseeable future. So they'll keep suppressing Palestinians (because they've got quite a tyrannic regime in Gaza), and do stupid things against Israel. Which then retaliates, and has also taken it as an excuse for other policies.
That cycle is not broken by some contorted, meaningless analysis using fashionable terminology. It will only make enemies in both camps. In a recent interview, John Gray said (about climate change, but it fits here too): "I think that’s the politics of narcissism: “I want to feel good.” But in the meantime, you’re wasting resources and you’re wasting time."
This conflict needs actions by a party with enough power to provoke a change on both sides. Ok, that's my bedside analysis, but the politically correct name calling (colonizer, fascist, terrorist) only widens the divide.
You surely know that pasting a dictionary definition is condescending, but I'll take a swing anyway.
Jews have a legitimate and ancient claim to indigeneity in the Levant. (In fact, this week's story of Chanukkah is about Jews being persecuted and evicted from from their homes in the region by a Greek empire.) Of course, Jews eventually left the region due to forcible diaspora.
Jews are obviously not the only ethnic group with a legitimate claim to the land. At least the following groups can all claim to be native to the land, for some definition of native: Turks, Ottomans, Arabs, and yes, Palestinians.
In a very real sense, the millions of Mizrahi Jews are in fact refugees from Arab countries (especially Yemen and Morocco), who fled persecution to their ancestral homeland.
But calling Israeli Jews settlers -- especially within the UN Green Line! -- is terribly inflammatory, and not particularly accurate.