As Neko stated previously Aset is not a goddess of the moon, sun, universe, and sea. Isis however is. This all goes into the debate on the differences between Isis and Aset, but I'll try to simplify it. Aset is an Egyptian goddess, Isis is a Roman/Greek goddess based on Aset. Isis can be a goddess of the moon, sun, universe, and the sea, because the Greek/Roman mindset equated Isis to Hera. Aset, however, is a goddess of the river Nile, a goddess of magic, a goddess of life, a goddess of mourning, a mother goddess, etc. There were no Egyptian gods of the sea, though there is a mention of a foreign sea god in the New Kingdom. Egyptians (before the Greeks came in and took things over) had little interest in the sea, it was basically a large, unending river to them, and considered highly dangerous. That is why in the tale of the sea mentioned above, gifts were given to the sea in order to placate it and keep it from encroaching on them. Isis, however, can be prayed to for anything, as she encompasses all things (syncretism was rampant). Also, while Aset may have held power over the universe, sun, and moon by being Werethekau ("great of magic"), she was not a goddess of these things. That would be akin to saying that because I know how to paint, I am an artist.
Wesir/Osiris is a Lord of Ma'at/ma'at (along with several other deities), but as with Aset he is not a god of Ma'at or of ma'at. To be a lord of something or to be involved in the process of something, is vastly different from being a god of that thing. If anything Djehuti/Thoth is more so a god of truth, as it is he that writes down the truths revealed by the scales of ma'at at the Judgment of the dead, while Wesir only observes the process. Ma'at is also a lot more than just justice and truth, and she and it are pretty awesome.
As for the whole:
I've never seen Wesir misunderstood for being a dead god.
There is quite a bit of evidence against Yinepu/Anubis being the child of Nebthet; it is evidenced that this is a later add on whenever the need for a triad of gods at each nome and temple became necessary. It's widely believed that this occurred in the New Kingdom, which is how Plato carried over into the story of Nebthet tricking Wesir into making Yinepu.
Set wasn't a god of evil, even after he killed his brother, and has always been a god of both chaos and storms (storms are considered chaotic in sunny Egypt). He became an evil god slowly over time as the cult of Wesir, Aset, and Heru-sa-Aset flourished and gained importance, while at the same time the Hyklos foreigners came in, took over, and used Set as the premier deity of the two lands (as he was similar enough to Ba'al).
Haroeris is a Greek name for Heru-wer (Great Horus), who was and is not Heru-sa-Aset (Horus son of Aset). These are the two basic forms of Heru's, but each of them has at least five additional forms. The two were not mixed/confused until the New Kingdom, and then were massively so after the Greeks took over. The information you've given could be applied to nearly all the Heru gods.
It would be more accurate to say that Geb is the Earth, and Nut is the Sky, as these are the earlier deities who personify concepts rather than being more civilization based. Nut isn't really a goddess of the universe as the universe includes the Earth. However, Nut does encompass the heavens and the Duat (the Nether-/Under-world isn't under our feet).
Atum and Iusas (or Nebethetpet in other cases) is existent at the beginning, however Iusas (and Nebethetpet) are usually placed as personifications of the right hand of Tem/Atem/Atum. Tem-Ra is not a common syncretic deity, as first Amun took over Tem's job, then Ra came into the picture. (Although there are a few cases of Tem-Ra.) I wouldn't say Tem is the god of creation, so much as he is one of the Creator gods (there are several, and one of them is even female), the same as I would say that Iusas isn't the primordial goddess of birth so much as she is the personification of the feminine creation energy.
Overall it's not a terrible introduction, but more research will reveal a lot more about these deities.