i don't understand the KVL solution to this question?
1: Because the \$12\Omega\$ and the \$6\Omega\$ resistors are in parallel, and the current through the \$6\Omega\$ resistor is \$1A\$, then necessarily, the current through the \$12\Omega\$ resistor must be \$0.5A\$. Think about why that is.

2: The polarity of \$V_x\$ is completely arbitrary. Swapping the signs around would just put a negative in front of anywhere that it appears in the resulting equations. The "natural" polarity (due to the passive sign convention), however, is to mark it as done in the problem, since the current \$5i_x - 1.5\$ is drawn entering the resistor to the right.

3: Yes, and in fact, that's exactly where the answer to #1 comes from.