The system consists of the block, spring, and Earth. Since the incline is frictionless, mechanical energy is conserved.

[Q1] Let the zero of gravitational potential energy be the point where the block momentarily stops. The initial height of the block is $h = (d+x)\sin\theta$. Initial energy (block at rest): $E_i = U_g = mgh = mg(d+x)\sin\theta$. Final energy (block at rest, spring compressed): $E_f = U_s = \frac{1}{2}kx^2$. By conservation of energy, $E_i = E_f$:

$$mg(d+x)\sin\theta = \frac{1}{2}kx^2$$

Solving for $d$:

$$d = \frac{kx^2}{2mg\sin\theta} - x$$

[Q2] The block's speed is greatest when its acceleration is zero, which means the net force on it is zero. After contacting the spring, the forces along the incline are the component of gravity pulling it down ($mg\sin\theta$) and the spring force pushing it up ($kx'$), where $x'$ is the compression distance.

$$F_{net} = mg\sin\theta - kx'$$

For maximum speed, $F_{net}=0$.

$$mg\sin\theta = kx_{max\_v}'$$

The compression distance at maximum speed is:

$$x_{max\_v}' = \frac{mg\sin\theta}{k}$$