If Eliezer was amazed at her level of Chesed, why did not know for sure that she was the right girl?
Rashi: He did not yet know whether she was from Avraham's family or not.
Seforno, Malbim: He did not know whether she was acting out of genuine Chesed, or whether she did not perhaps expect some form of remuneration. 1
Rashbam: Indeed, the moment Rivkah informed him that she would draw water for his camels too, he knew for sure that Hashem had fulfilled his request. 2
Ohr ha'Chayim: He was concerned lest she is among those who say much, but do little. Therefore, he waited until they finished drinking.
What was the significance of his silence?
Seforno: It would have been correct for Eliezer to inform Rivkah not to go to so much trouble. But he didn't, because it was all part of the test.
Ha'Emek Davar: He should have spoken with her to gauge her intellect. However, while speaking one cannot observe every motion like while he is silent. Also, she could not act with such speed if she needed to answer him.
Why, now, does the Torah begin to call Eliezer "ha'Ish" (an expression of importance) instead of 'ha'Eved'?
Oznayim la'Torah: When he saw the open miracles that Hashem had performed with him, and acknowledged them, he was transformed from an Eved to an Ish, with nobody other than Hashem above him. 1
Indeed, the commentaries explain that, at the termination of his mission, Avraham set him free - This then, was the first stage of his freedom. (EC). Oznayim la'Torah