If you take the Eurostar (the train which travels to Europe via the Channel Tunnel), it is at St Pancras International station, about an hour on the Underground from Heathrow, and you need to check in an hour ahead of departure time. That is because after check in you have airline type security checks, then UK departure border checks (have your passport out and available) and then French border checks (because they are the first country that your train arrives in, even if you are going to Amsterdam, coming out of the tunnel you are in France) (have your passport out for them too) before you can get to the waiting room where you wait for your train to be called.
So, to directly answer your last question, no the train is not at Heathrow. Some people will tell you to take the Heathrow Express train from Heathrow to Paddington station, and then get a cab or tube train to Kings Cross/St Pancras but I believe that it is just as easy, just about as fast, and much cheaper just to get on the Tube at Heathrow and get off at Kings Cross/St Pancras and go upstairs for your train.
You have already heard of the difficulties and expense of taking a plane to Amsterdam on a separate booking. That applies for both train and plane, but at least if you are at Heathrow already you don't have far to go to get to your plane and when it goes it is considerably faster than the train.
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