When did she become famous for her beauty?
Radak: This was in the kingdom of David and Shlomo. Malbim ? it says "va'Yetzei Shem David b'Chol ha'Aratzos" (Divrei ha'Yamim I, 14:17). All nations used to bring gifts to Shlomo
What is "Kalil"?
Rashi #1: It is an expression of Michlol (perfection or splendor).
Rashi #2: It is complete [Radak ? with all kinds of beauty and glory].
Rashi #3: It is a crown. The Targum of "Nezer" (Shemos 29:6) is Kelila.
Why does it say "ba'Hadari Asher Samti Alayich"?
Radak: All this great success that you had in these days was with My help. You did My will, and I made you rule over the nations. It was not due to your strength.
Malbim: The beauty was not your own I put it on you. I.e. via Hashgachah ? Hashem's honor appeared on you.