Why did Eliezer omit that he prayed that he would say to the girl, "Hati" (24:14), but then he said "Hagmi'ini" (24:17)? (Here, he reports that both times he said "Hashkini"?) Also, he did not report that she did not offer to give to the camels until after he drank, which was unlike his prayer?
Ha'amek Davar: He did not want to give to them room to say that it did not happen just like he said (so they should not give Rivkah).
In his Tefilah (24:14), Eliezer had said "Na'arah." Why did he say now "Almah"?
Malbim: Eliezer concealed that he intended for a girl from a poor family. Almah implies a healthy girl (i.e. from a distinguished family).
Ha'amek Davar: He did not want to give to them room to say that she is not a Na'arah. 1 "Almah" can be also a minor.
This is like Kesuvos 40b: R. Meir holds that Na'arah is an adult (within six months after Bas Mitzvah). Rabanan disagree only when the word Na'arah is written Chaser (without a Hei), to include a minor. (In this entire Parshah, 'Na'arah' is written Chaser.)
