3. D

As shown in Figure 7, in the cube $A B C D$ $A_{1} B_{1} C_{1} D_{1}$, $A A_{1}$, $B C$, and $C_{1} D_{1}$ are pairwise skew lines. Take any point $F$ on $C_{1} D_{1}$, and connect $A_{1} F$. Draw a line through point $A$ parallel to $A_{1} F$ intersecting $B C$ at $E$, and connect $E F$. The line $E F$ must intersect the line containing $A A_{1}$. By the arbitrariness of $F$, it can be seen that there are infinitely many lines that intersect $A A_{1}$, $B C$, and $C_{1} D_{1}$, and these infinitely many lines are also skew.

As shown in Figure 8, take any point $P$ in plane $M$, and draw three lines $a$, $b$, and $c$ through point $P$ that are parallel to three pairwise skew lines and parallel to $M$. Since the angles formed by the three lines are equal, and among the four angles formed by the intersection of $a$ and $b$, there must be one pair of vertical angles that are acute or right angles. Therefore, line $c$ must be the angle bisector of the other pair of vertical angles. Hence, the angle formed by the three lines is $60^{\circ}$.

As shown in Figure 9, in the rectangular prism $A B C D$ $A_{1} B_{1} C_{1} D_{1}$, $A B$, $B_{1} D$, $A_{1} D_{1}$, and $O C_{1}$ are pairwise skew lines. Connect the diagonal $B D_{1}$, which must intersect $D B_{1}$. Let the intersection point be $O$, then $B D_{1}$ intersects $A B$ at $B$ and $A_{1} D_{1}$ at $D_{1}$. Denote $B D_{1}$ as $l_{1}$. Then take any point $M$ on $C_{1}$, and connect $D_{1} M$, denoted as $\iota_{2}$. There are infinitely many such $\iota_{2}$. Therefore, there are infinitely many pairs of intersecting lines that satisfy the conditions.
3. Proposition 1: If 3 lines are pairwise skew, there can be infinitely many lines that intersect all 3 lines, and these infinitely many lines are also pairwise skew.
Proposition 2: If plane $M$ is parallel to 3 pairwise skew lines, and the angles between the 3 lines are equal, then the angle between the lines is $60^{\circ}$.
Proposition 3: If 4 lines are pairwise skew, and a pair of intersecting lines $l_{1}$ and $l_{2}$ are constructed such that $l_{1}$ intersects one pair of the skew lines and $l_{2}$ intersects another pair of the skew lines, such pairs of intersecting lines can be infinitely many. The number of correct propositions is ( ).
A. 0
B. 1
C. 2
D. 3