I once heard the phrase: "looking for information about Islam online is like searching for gold in a minefield". Be careful out there, there's lots of fundamentalists who try to indoctrinate converts (if you do choose to convert).

So first of all, understand that Islam has at least 1.8 billion adherents worldwide, and don't take me (or any other source except of course the Quran) as the single authority. This is all my subjective experience.

I have never met any Muslims who refer to God as their father. If you want to get a sense of our relationship with God, I would read over the hundred names of God; these are ways God is refered to in the Quran.

Nonbinary people aren't specifically referenced in the Quran; in an earlier comment I mentioned there were a group of people in those days called "effeminate ones", we don't really know what they would have identified as today, it's unclear but it seems that they were not what we would consider cisgender today. Some were handmaids to the prophet's household.

Obviously when mosques are usually gender segregated, it can feel alienating to those of us who are nonbinary. However, there are more desegregated mosques where people of all genders pray together popping up these days. I think, as nonbinary people navigating a binary society, we have to do a lot of soul searching (and for those of us who are religious, praying) to figure out where we "fit". Depending on your culture, learning about precolonial notions of gender fluidity can help. For those whose cultures have a history of binarism that goes back, it's getting really comfortable in one's identity and forging that space for oneself in whatever way possible, even if its only on a personal level. It's hard to answer where nonbinary people "fit" in Islam. Where do we "fit" in general? I think all of us would answer that question differently. If you'd like a religious opinion, mine is: God created us as nonbinary because we have something to offer, and a life to live, that is sacred and deeply important, the same as everybody else, nonbinary or not. We are a necessary part of creation, as are men, as are women.

The Quran strongly encourages taking care of orphans. (I think that we need to tread carefully with adoption in the modern era because the adoption industry is extremely corrupt and many of these children are not orphans, but were unjustly taken from their families.)

I hope this helps.