***** NOT A TEACHER *****
Here is some information that may interest you.
THE CHICAGO MANUAL OF STYLE is a book that many American writers follow. I have the 1993 edition, but you can find the newer editions in a good bookstore or probably online.
“If a dependent clause is restrictive – that is, if it cannot be omitted without altering the meaning of the main clause – it should not be set off by commas. If it is nonrestrictive, it should be set off by commas.”
It then gives these examples:
- Paul was astonished when he heard the terms.
- At last she arrived, when the food was cold.
The book does NOT explain the difference. It leaves it to us to interpret the difference.
In No. 1, I guess the adverbial element is restrictive. If we removed it, we would “alter” the meaning of the sentence. Q: When was Paul astonished? A: When he heard the terms. (Not when he saw that the doughnuts were stale, not when he heard that his favorite actress was getting married, etc.)
In No. 2, “when the food was cold” is just an extra comment thrown in by the speaker. In other words, the person arriving late did not think to herself: I have decided to arrive when the food is cold." It was just a coincidence.
I certainly do NOT have the confidence to pronounce on the “correctness” of your three sentences.
So you should ask yourself, is the adverbial clause necessary to explain the main sentence? If it is, then do not use a comma.
By the way, I also think that in speaking, the pause (comma) plays a big role. For example, I am pretty sure that speakers would pause in saying No. 2. “At last she arrived – when the food was cold.” The speaker is being sarcastic and expressing his / her own opinion. It is NOT a restrictive clause.