Rules question Twilight Struggle

I just purchased Twilight Struggle and I'm currently trying to get a hang of the rules but I still have a couple of questions.

The first one is regarding playing cards for ops/event.

As far as I've understood it you play a card for your own faction EITHER fot OPS points OR the event.

With a dual action or a card for the opponents faction you play BOTH the Event effect AND the Ops points.

Is this correct?

Also I have no idea how the China card works, it's not part of either players hand but switches factions each turn and only affects the one faction which controls it, but what's the whole deal about flipping it sometimes?

Help is much appreciated!