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I don't have Munkres' book. So I don't know what is done there. You should probably consult the "Counterexamples in Topology" as mentioned above.
My favourite book for questions of this type is "General Topology" by Ryszard Engelking. It has a diagram in the back with interrelations between different properties of topological spaces. It has all the notions you are interested in, except the last two. Local compactness and various additional versions of paracompactness are also discussed in the book. I assume, but haven't checked in every case, that the relations in the diagram are proved in the book. The book also contains plenty of examples, showing that certain implications do not hold, sometimes in the form of exercises with hints.
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I don't have Munkres' book. So I don't know what is done there. You should probably consult the "Counterexamples in Topology" as mentioned above.
My favourite book for questions of this type is "General Topology" by Ryszard Engelking. It has a diagram in the back with interrelations between different properties of topological spaces. It has all the notions you are interested in, except the last two. Local compactness and various additional versions of paracompactness are also discussed in the book. I assume, but haven't checked in every case, that the relations in the diagram are proved in the book.