Questions about Neural Network training (back propagation) in the book PRML (Pattern Recognition and Machine Learning)
As you point out, with $\delta_k = y_k - t_k$, the author is stating the relationship between the final units' output and the target. So Equation 5.54 is simply stating:


  the error on the $k^{th}$ output unit is the difference between its output and the target.


I believe that $\delta_k$ refers to the error simply at the output, whereas $\delta_j$ is the derivative of the output at unit $n$ with respect to any neuron back in the network, $j$. If this is the case, doing your derivative as you did, for $\delta_k$ (instead of $\delta_j$) means you are computing the error gradient between the output and the final layer. Over this layer, the activation must be linear (we do not apply a non-linearity at the final layers output). This would mean your 
$\dfrac{\partial h(a_k)}{\partial a_k}$ term would actually fall away in this case (to a constant), using the $k$ subscript - and you have the answer from the author: $y_t - t_k$.



The network that is considered in your second question seems to only really discuss a single fully-connected layer, so yes, two actual layers of neurons - input and output only with no activation (so a linear activation, as you mention).