Interesting. Bahn.com shows the 1818 as a connection - although not official I assume it's using something to generate its times?
Trainsplit suggests
1802-1803 Walk to King's Cross
15 minute wait
1818 to Newcastle
but I guess I'm supposed to add 15 minute connecting time at St Pancras International before that?
In reality, I'd probably book the 1830 departure, which is a couple of quid cheaper.
Having arrived back to St Panc recently from Paris, I'd definitely suggest the 18:30 is the earliest to get. If you are in the first 2 or 3 coaches from the buffers, then you
might make the 18:18, but even then you'd have to be one of the first off the train, as people disembark and just stand still (seriously !).
As for arriving at St. Panc for the outward journey. I've never had a problem arriving 45 minutes before departure. Make sure you are organised though. Coat, belt etc off and packed in bags for security. The staff are pretty good at making sure you get to your train. Again it is not the process that is the issue, it is other people who are clueless. Boarding normally starts around 25 minutes before departure.
Only issue I ever faced was when trains got cancelled, then St Panc looks more like a refugee center than a railway station.