"words to numbers" is the secret sauce of all the models including the new GPT-4. Individual words are tokenized (sometimes into "word pieces") and a mapping from the tokens to numbers via a vocabulary is made. Then the model is trained on pairs of sentences A and B. Sometimes the model is shown a pair where B correctly follows A, and sometimes not. Eventually the model learns to predict what is most likely to come next.

"he went to the bank", "he made a deposit"

B probably follows A

"he went to the bank", "he bought a duck"

Does not.

That is one type of training to learn valid/invalid text. Another is "leave one out" training. In this case the input is a full sentence minus one word (typically).

"he went to the convenience store and bought a gallon of _____"

and the model should learn that the most common answer will probably be "milk"

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Back to your first question. In 3D your first two embeddings should be closer together because they are similar. And they should be both "far' from the third encoding.