Rosh Chodesh Questions

What's the big deal about Rosh Chodesh, the "New Moon," when the moon is hardly visible; shouldn't we celebrate instead the middle of the month when the moon is round and perfect?

Why is Rosh Chodesh, the holiday that marks the entry of a new Jewish month, considered a "women's holiday"?

The practice of the Sanhedrin in ancient times is the reason for Rosh Chodesh being one or two days -- depending on the month.