Silmarillion - Chapter 11 - Of the Sun and Moon and the Hiding of Valinor

[Estelyn Telcontar]

In reply to your first paragraph, there are differences in the perceived genders of sun and moon in different languages. In German, for example, the sun is female and the moon male (die Sonne, der Mond). On the other hand, Lewis Carroll has the opposite in one of his (English, of course) nonsense poems - despite the fact that there is no mandatory gender of the words in English:

The sun was shining on the sea,
Shining with all his might:...

The moon was shining sulkily,
Because she thought the sun...

(The Walrus and the Carpenter)

In Arda, the sun is guided by Arien, a female Maia - perhaps that is the reason for Tolkien's choice. The moon is guided by Tilion, a male Maia. An additional factor could be the traditional "man in the moon", also used by Tolkien in some of his lighter poems.