decision rule for image segmentation
1) Yes, your solution is correct.

2) If you assume that all a priori probabilities are equal, then the boundaries for AWGN is always the middle points between the possible values of X.  In this case, then, the decision boundaries are at 75 and 175.

I believe that this rule (decision boundary at the middle points) can be generalised to applying to any noise probability distribution that is symmetric and monotonically decreases as the distance from zero increases.