Why are there infinitely many indifference curves?
Utility is constant for all points $(q_B,q_A)$ on an indifference curve. So there is a number $u_1$ such that 
$$
\forall (q_B,q_A) \in IC_1: \ U(q_B,q_A) = u_1.
$$
Similarly there is a number $u_2$, such that
$$
\forall (q_B,q_A) \in IC_2: \ U(q_B,q_A) = u_2.
$$
If $IC_1 \neq IC_2$ then $u_1 \neq u_2$.