Why did Eliezer prostrate himself?
Rashi: To thank Hashem for the good news that he had just heard. 1
Ha'Emek Davar: He fully prostrated on the ground, and did not merely bow, due to great Simchah and gratitude.
See Sifsei Chachamim as to why Rashi did not make the same comment above (on Pasuk 26).
Why did Eliezer thank only Hashem, and not her father?
Malbim: [Her family] admitted that it was from Hashem, and does not depend on their will.