Current state of SegWit and Bitcoin Core?

I've done some reading about SegWit and how it is generally desirable to use because it allows for much lower fees (and a bunch of other stuff). I'm running Bitcoin core and using a core wallet so I am most interested in using SegWit with core.

Reading about SegWit, I see mentions of "will soon be compatible" or "coming soon" type of language. Is that just old language? Is SegWit now fully supported in Bitcoin core?

This post at stackexchange says SegWit won't be live on the network until Nov 15. I notice that date is very close to the approximate date that the Segwit2x fork goes live. Is that coincidence or are both events triggered by the same conditions?

TL;DR is SegWit currently supported in Bitcore Core today?