Elvish Reproduction

[Thinlómien]

Also, does it seem that there are always more Elf males being born? Feanor has no daughters, for example, and Galadriel was the only daughter. Can we safely assume that female Elves tend to give birth to more males than females?

I don't think so. Having a lot of sons (and maybe one daughter) is just usual stuff of legends and tales. Maybe we shouldn't think the "gender-balance" with the lords of eldar as an good example of elvish "gender-balance" but just parts of the story.
The non-famous elves had all the daughters...

And about yhe menstruation: from all your "conclusions" maybe once a year in a period of 100-300 years after getting married?