Given OP = i − 3j, so the position vector of P is 1 -3 .

Step 1: Express the given vectors in component form.
Given $OP = i - 3j$, so the position vector of P is $\begin{pmatrix} 1 \\ -3 \end{pmatrix}$.
Given $PQ = 4i - 2j$, so the vector from P to Q is $\begin{pmatrix} 4 \\ -2 \end{pmatrix}$.

a) The coordinates of Q.
To find the position vector of Q, we add the vector $OP$ and the vector $PQ$.

$$OQ = OP + PQ$$ $$OQ = \begin{pmatrix} 1 \\ -3 \end{pmatrix} + \begin{pmatrix} 4 \\ -2 \end{pmatrix}$$ $$OQ = \begin{pmatrix} 1+4 \\ -3-2 \end{pmatrix}$$ $$OQ = \begin{pmatrix} 5 \\ -5 \end{pmatrix}$$

The coordinates of Q are $(5, -5)$.

b) $|PQ|$ in surd form.
The vector $PQ = 4i - 2j$.
The magnitude of a vector $v = ai + bj$ is given by $|v| = \sqrt{a^2 + b^2}$.
For $PQ = 4i - 2j$, we have $a=4$ and $b=-2$.

$$|PQ| = \sqrt{4^2 + (-2)^2}$$ $$|PQ| = \sqrt{16 + 4}$$ $$|PQ| = \sqrt{20}$$

To express this in surd form, we simplify $\sqrt{20}$:

$$\sqrt{20} = \sqrt{4 \times 5}$$ $$\sqrt{20} = \sqrt{4} \times \sqrt{5}$$ $$|PQ| = 2\sqrt{5}$$

The final answers are:

a) The coordinates of Q are $\boxed{(5, -5)}$.

b) $|PQ|$ in surd form is $\boxed{2\sqrt{5}}$.