Why did he say that Shlomo is "Na'ar va'Rach"?
'Rashi': Even a 42 year old is called Na'ar ? "Yehoshua bin Nun Na'ar Lo Yamish mi'Toch ha'Ohel" (Shemos 33:11). He lived 28 years after Moshe died, to the age of 110. It turns out that in the second year that Yisrael were in the Midbar (when this verse was said), he was 42. Here it says "Rach", for Shlomo was only 12 years old 1 when he became king.
Gra, Malbim: Na'ar means that he is young. Rach means that he has a delicate nature, like "ha'Rakah veha'Anugah" (Devarim 28:56).
Radak (29:1): Seder Olam (14) says so. Amnon raped Tamar about when Shlomo was born. Avshalom killed Amnon two years later, and fled to Geshur for three years. He returned, and rebelled two years later. After were three years of famine. The next year (Shlomo's 11th year), David counted Yisrael; this took nine months (Shmuel II, 13:23, 38, 14:28, 21:1: 24:8). In David's last year (his 40th year of kingship), he established Mishmaros. (This is unlike Radak wrote in Shmuel II, 15:7, that Avshalom rebelled in David's 37th year! ? PF)
Why does it say "Lehagdil l'Ma'alah"?
'Rashi': It will be very tall ? 120 Amos (Melachim I, 6:3).
Gra: This is like the verse continues, "l'Shem ul'Sif'eres." We do not aggrandize and beautify Beis Elokeinu because He needs its light, or our glory. Rather, we aggrandize and beautify the Beis ha'Mikdash that it will be greater than all buildings, so awe and fear of Him will fall on all who see. They will publicize for glory to all lands.
Malbim: Since Hashem will dwell in it, it must be great, and also "l'Shem ul'Sif'eres l'Chol ha'Aratzos" ? glorious in the eyes of the nations.
