A: A more common name for the book is "The Stevens Book". Rich Stevens is one of the heroes of the computer field (I should probably say "was", he passed away recently), and his books are respected reference works.
B: To debug this problem, you'll need to know how the interface to the compiler works, and what the difference between compiling and linking (a.k.a. loading) is. You need to understand that to read the make file. You also need to get at least a cursory overview of how make works, and how to translate the make file into the commands that will actually be executed.
C: The error messages you are getting are completely obvious: you are trying to link the object file lsnew-b101a.o into an executable, and in the process the linker complains that it doesn't have a copy of the functions err_quit and err_sys. That clearly means that something is wrong on your linker command line. Most likely the make file is screwed up. Perhaps the make file is not intended to be used with this particular flavor of make (see the comments above about the differences between gmake = Gnu make = the default make on Linux, and the default version of make that ships with the *BSD operating systems), or perhaps the make file is not intended to be used with your compiler (which is clearly clang/llvm judging by the error messages, while most of the Linux world uses gcc = the Gnu compiler).
D: I just copied the file you posted above into apue_test.c. Then I downloaded apue.h from github (it seems someone has posted all the example code from the book there, whether legally or not I don't want to think about). Instead of using make, I compiled the file apue_test.c by hand, using the following command: "cc -c apue_test.c", which created apue_test.o. I gave no errors, only one warning (about sys/termios.h being deprecated, which we can safely ignore). Then I tried to link the file test.o into an executable using the command "cc apue_test.o -o apue_test", which obviously failed complaining that it is missing err_quit and err_sys (which is completely expected, you got exactly the same errors). That demonstrates that the source file above is in good shape, but that it needs to be linked against another object file or library that contains those two functions.
Suggestion: Before you learn about advanced programming, you need to study toolsmithing, and how to operate tools like compilers, linkers, and make. I would suggest that you write yourself a pretty simple program from scratch (maybe a slightly advanced version of "hello world" that parses the command line and calls a function, with the function in a separate file and a header file for it), and write a make file for that from scratch, and get that to work first.