You are correct in your understanding that the smallest possible amplitude of the resultant wave is Y1 + Y2 when the two waves are 180 degrees out of phase. This is because when two waves are 180 degrees out of phase, the crests of one wave align with the troughs of the other wave, leading to cancellation and a smaller resultant amplitude.
For the second question about the speed of the wave, you correctly use the formulas for wave speed (v), wave number (k), angular frequency (w), and wavelength (lambda). The formula v = w/k relates the speed of the wave to its angular frequency and wave number. Since k = 2pi/lambda, you substitute this value for k into the equation and get v = w/(2pi/lambda). Simplifying this expression, you can rearrange to v = w * lambda / (2pi). From this equation, you can see that the correct answer is b) w/K, which matches your initial choice.
Therefore, your answers are:
1) a) Y1 + Y2 and occurs if they are 180 degrees out of phase, and
2) b) w/K