Again, there are two different meanings of the word discriminate. Having different bathrooms is discriminating between the genders. Treating them differently. Having bathrooms for one gender and not the other would be discriminating against that gender.

No, there are two word, discrimination and segregation. Men having a bathroom and women not (or vice versa) would be discrimination: one have bathroom, other don't. In having separate bathrooms men have a bathroom and women have a bathroom, no discrimination there.

No, this not even something we have to argue about. Simply look up the definition of the word:

http://www.merriam-webster.com/dictionary/discrimination

This conference is about the first definition, not the third.

Segregation on an axis requires discrimination on the same axis (if you don't make distinctions, you can't separate.)

> Treating differently by "distinctions" is discrimination, not just making them.

Segregation is treating people differently by the axis on which segregation occurs.