Differentiation - Connected Rates of Change

The equation of a curve is given by \(y = (x - 5)(2x - 1)^3\).

1. Express \(\frac{\mathrm{d}y}{\mathrm{d}x}\) in the form of \((ax + b)(2x - 1)^2\), where \(a\) and \(b\) are integers.
2. Given that \(y\) is increasing at a constant rate of \(0.25\) unit/s, find the rate of change of \(x\) when \(x = 2\).
3. Another curve has the equation of \(z = y^2\). Show that when \(x = 0\), \(z\) is increasing at \(10\) times the rate of \(y\).