What is the significance of the word "Re'ei"?
Rashi (B'rachos, 55a) and Ramban #1: It means 'Take note! of the wonder that any one person, even if he was well-trained, should be an expert in so many facets 1 is hard to conceive. The fact that he had never even seen them being performed is even more incredible. And when one considers that Betzalel grew up in a society who labored in mortar and cement, and was a mere thirteen years old, it is truly mind-boggling. Hence when Hashem presented Betzalel to Moshe, he declared "Re'ei ... !". 2 And Hashem wanted Moshe to realize that He had filled Betzalel with His Spirit - even when he was still in his mother's womb. 3
Ramban #2 (citing Midrash): Hashem showed Moshe the Seifer of Adam ha'Rishon, and pointed out how, already at that stage, He had designated by name, the leaders of each and every generation (including Betzalel in his generation).
In silver, gold, precious stones, wood, embroidery and weaving. Moreover, Betzal'el knew all the deep meanings (Chochmah, Binah and Da'as) of everything that he manufactured (not to mention the ability to impart the knowledge to others - Ramban). See also Ibn Ezra.
And that explains why, when Moshe presented Betzalel to Yisrael (35:3), he too declared "Re'u ...!" (Ramban).
As in Yirmiyah, 1:5 (Ramban).
What are the connotations of "Karasi be'Shem"?
Rashi: It means that Hashem called Betzalel to do His work". 1
Ramban #1: Refer to 31:2:1:1.
Ramban #2 (citing Midrash): Refer to 31:2:1:2.
Targum Onkelos: It means that Hashem elevated Betzalel.
Targum Yonasan: It means that Hashem called Betzal'el by that name because it was the name that suited him (since it is the acronym of "be'Tzeil Keil Hayisa'). 2
B'rachos, 55a: It means that Hashem appointed Betzal'el as the chief architect - and this teaches us that Hashem tends to announce good communal leaders personally. 3
Why was Betzalel, the grandson of Chur - chosen to build the Mishkan to atone for the murder ot Chur, and not Uri his son?
Oznayim la'Torah: Because Uri was in mourning over the death of his father, and the Shechinah (which instructed Betzalel how to construct the Mishkan), 1 would not have rested on him, since the Shechinah only rests on someone who is happy.
As the following Pasuk tells us.
Bearing in mind that, based on the Pasuk in Vayakhel, 36:4, which refers to Betzalel (ben Uri, ben Chur ben Calev, as "Ish", he was at least thirteen when he built the Mishkan, how could Calev, who was forty (See Yehoshu'a 14:7), have a great-grandson of thirteen?
Sanhedrin, 69b: We see from here that the early generations were able to have children from the age of eight. 1
See Torah Temimah citing Sanhedrin, 69b, and note 6.
Why does the Torah mention even Betzalel's grandfather (Chur), and for Ohali'av, only his father?
Da'as Zekenim, Hadar Zekenim and Moshav Zekenim: Because Chur was murdered when he [protested against] the Eigel, and the Mishkan comes to atone for his murder.