Fauda looks shady.

1. The name "fauda" is Arabic for "chaos". "Anarchism" has been translated into Arabic as "chaosism" but sane anarchists should reject this term. But maybe they meant something different with it.
2. In this interview https://intimitescriminelles.noblogs.org/?p=61 they say

Unfortunately, Israel’s security systems interpret all our work, even our humanitarian work, as security threats. That’s why we don’t publish photos and videos of many of our actions, such as going to prisoners’ homes.

This article also defends their "security culture" https://rant.li/alks/on-palestinian-anarchists-fauda But in that interview they also say

Supporters of Palestine can helps us in 2 ways: 1- print our flag (fauda flag) and go into the street with friends and make videos. We will share these videos so our people see world supporters

3. They seem supportive of hamas in a certain way even though they constitute an authority. So when you cooperate with hamas and you're done with Israel you'll just fight hamas after they rise to power?

This article makes some big accusations I haven't checked them all https://avtonom.org/en/news/fake-chaos-fauda-so-called-organization-palestinian-anarchists But some of them are addressed here https://rant.li/alks/on-palestinian-anarchists-fauda

As far as I know proper anarchism has absolutely no history in Iraq. Trust me, I searched a lot. There are socialist and communist parties but after the fall of Saddams regime they don't seem to have gone through suppression. Members of the PKK have libertarian tendencies but that's a very different discussion. However there is precedent for suppression. Internet shutdowns during times of unrest are normal. Security forces roam the streets and last time I checked it is illegal to insult (some of) them. Torture exists. Some political parties have their own militias. Sorry, but this is all I know.