With regard to the Sun and Moon comments, there are two things to consider:
1) Why a feminine sun and masculine moon
2) What this means for the Hobbits' knowledge
The reference to a feminine sun and masculine moon harkens back to older traditions that are still present in a vestigial form in English. In the West, a feminine sun appears in German tradition and other traditions of the north, such as Scandinavia and Iceland.
Following this lead, Tolkien adopted the notion of a feminine sun and a masculine moon for Middle-earth, following the Germanic tradition.
The notion of the feminine sun and masculine moon subverts current conventions in English that bury the old tradition, (though the English word "Sun" actually comes from a feminine origin).
In Germany, popular tradition still refers to Frau Sonne. The very word “Sun” comes from the name of the Scandinavian Sun-Goddess Sunna or Sunnu. Sunday, of course, is Her day. Just as Friday is a contraction of Freya’s day, Sunday is a contraction of Sunna’s Day.
for a fuller discussion.
Wiki has some info on this as well: Sól (Sun) - Goddess
Máni (Moon) - Moon God
With regard to the question of what this means for Hobbits' knowledge of the true state of affairs in Middle-earth, I am not certain.
However, I would not be surprised to hear that linguistic conventions like this could be adopted and persist without a deeper knowledge of the "true affairs".
How many here knew that the English word "Sun" actually had a feminine derivation, and the "Moon" a masculine derivation?
To me, the whole affair, including the footnote, is just another philological in-joke by Tolkien, since the whole poem itself represents a proto- or ur- version of the familiar nursery rhyme.
In this respect, the poem is a microcosm of what he was trying to achieve with his mythology as a whole. The whole of the mythology attempts to be a kind of representation of all of the common themes of gods, elves, dwarves, men and other strange creatures on the boundaries of faërie (properly conceived), and that we now only perceive in fragments.
This is why Middle-earth feels so real to so many. In the same way, one can look at the Man in the Moon poem and imagine that if it was largely forgotten, that the snippets that we have in "nursery rhyme" form would be all that was left.
My niece, Humera, under a pumpkin leaf!