Yes, you can do that.

There is a slight gray area if the kid is under 100%, but that doesn't apply to your situation (and the IRS has allowed it since it started in 2014 anyways).

Yeah, I probably turned off messaging on this forum to avoid DIYers trying to message me.  As for Facebook, I didn't see anything and I don't know why you couldn't do that.  I get Direct Messages from other people.