Each of the 3 Pesukim in Birkat Cohanim consists of 2 Brachot. Here is how Rashi describes them:
- יברכך. שיתברכו נכסיך
- וישמרך. שלא יבואו עליך שודדים ליטול ממונך
- יאר ה' פניו אליך. יראה לך פנים שוחקות, פנים צהובות
- ויחנך. יתן לך חן
- ישא ה' פניו אליך. יכבוש כעסו
- וישם לך שלום
The בעל הטורים brings a proof to there being 6 blessing:
אמ*ו*ר להם - מלא - כנגד ו' ברכות יברכך,וישמרך, יאר, ויחנך, ישא, וישם שלום. כנגד ו`. תורת י"י עדות י"י ופקודי י"י מצות י"י יראת י"י משפטי י"י
(בעל הטורים - במדבר ו-כ"ג)
They are one of the few examples in the Torah of a Bracha; wishing somebody health, wealth and peace, etc.
Other examples are the blessings that Yitzchak wished upon Yaakov and Eisav, and the blessings Moshe gave the Yidden at the end of his life.
Not to be confused with the "Baruch Ata" type of Bracha which is either thanking or praising Hashem for something.
Other points you raised:
keyn yehi ratzon: That's because the Chazan is not really giving a direct Bracha. He says "Bless us with the threefold Bracha written in the Torah; Yevarechecha, etc.", so we answer "may it be [His] will"; we can't answer Amen since there was no direct "wish".
As opposed to the Cohanim who are actually blessing us, so we answer "Amen".
baruch hu u'varuch shemo is frowned upon by many Poskim - when the Cohanim are blessing us - since it's a Hefsek. Other Poskim seem to allow it, judging by common practice.
blessing the children on Shabbat they usually don't answer Amen either out of habit, since they havbe been blessed this way since before they could talk, or else because it's often said quietly. Lately my kids have started saying Amen when they figure out I'm done (by lifting my hands off their head); I have no idea what prompted that behavior.