1)
Why did Eliezer prostrate himself?
1.
Rashi: To thank Hashem for the good news that he had just received. 1
1
See Sifsei Chachamim as to why Rashi did not make the same comment earlier in Pasuk 26.
2)
What are the implications of ?Vayishtachu Artzah ? ??
2.
Ha'amek Davar: He fully prostrated hiself on the ground, and did not merely bow down, due to great Simchah and gratitude
3)
Why did Eliezer thank only HaSh-m, and not her father?
1.
Malbim: [Her family] admitted that it was from HaSh-m, and does not depend on their will. 1
1
Also refer to 24:53:151:1.