Is support vector machine with linear kernel the same as a soft margin classifier?
The idea of soft margin classifier means that one allows a number of misclassifications on the wrong part of the margin. This has nothing to do with the used kernel. Using a linear kernel or other type of kernel only affects in which kind of space the separating margin is searched. All SVMs uses soft margin, but one can push the soft margin behavior towards a hard margin behavior but imposing a very large penalty on errors.
Linear SVMs either for regression or for classification have a special characteristic. The numerical computations are simpler because one can compress the original result of the algorithm into a much simpler formula (due to it's linearity). This is why often implementations for SVMs and SVCs have sometimes separate implementations for the linear kernel.
No. The two are independent of each other.
The kernel $K(x, z)$ is the generalisation of the scalar (dot) product, $x \cdot z$. We often choose $K(x, z)$ to be a non-linear function (polynomial, RBF, etc.). If not, i.e. if $K(x, z) = x \cdot z$, we say that the kernel is linear.
Independently of the kernel, a classifier can use a hard or a soft margin. A hard-margin classifier requires the classes to be linearly separable in the kernel-induced feature space. For the linear kernel this is the same as simply saying that the classes are linearly separable, but a non-linear kernel can also transform non-separable data into separable ones.
A soft-margin classifier can tolerate misclassification of some observations, making it suitable for training even if the data are not separable.
So, the choice of the kernel and the choice between the hard or soft margin are two distinct choices you need to make. In practice we almost always use soft margin, but control for its "softness" using the parameter $C$. As $C \rightarrow \infty$, the margin approaches the hard margin.
From what I have understood, and also from what the author of this book is telling here, a linear kernel is another representation of the support vector classifier. As he adds in the end, when the support vector classifier is combined with a non-linear kernel (polynomial/RBF) we have a support vector machine. SVCs and SVMs use a soft margin whereas only a Maximal Margin Classifier uses a hard margin, which is different from a support vector classifier.