It seems that Apple keeps on moving their tools around and the old solution of installing the command line tools are with using xcode-select --install doesn't work.
In Mojave, xcode-select doesn't install anything anymore (the GUI always fails to find the package) and the command line tools don't install itself in /usr/ or /usr/local.
xcode-select --install did work for me in Mojave. Maybe you can try installing XCode from Mac App Store, and then install developer tools?
Regarding header locations, I have Apples headers in /Library/Developer/CommandLineTools/:
$ sudo find /Library -name stdio.h
/Library/Developer/CommandLineTools/usr/include/c++/v1/stdio.h
/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/sys/stdio.h
/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/stdio.h
/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/System/Library/Frameworks/Kernel.framework/Versions/A/Headers/sys/stdio.h
And if you install gcc via brew, it will add headers in /usr/local/:
$ sudo find /usr -name stdio.h
/usr/local/Cellar/gcc/8.2.0/include/c++/8.2.0/tr1/stdio.h
/usr/local/Cellar/gcc/8.2.0/lib/gcc/8/gcc/x86_64-apple-darwin17.7.0/8.2.0/include/ssp/stdio.h
/usr/local/Cellar/gcc/8.2.0/lib/gcc/8/gcc/x86_64-apple-darwin17.7.0/8.2.0/include-fixed/stdio.h
/usr/local/Cellar/gcc/8.1.0/include/c++/8.1.0/tr1/stdio.h
/usr/local/Cellar/gcc/8.1.0/lib/gcc/8/gcc/x86_64-apple-darwin17.5.0/8.1.0/include/ssp/stdio.h
/usr/local/Cellar/gcc/8.1.0/lib/gcc/8/gcc/x86_64-apple-darwin17.5.0/8.1.0/include-fixed/stdio.h
/usr/local/Cellar/gcc/7.3.0_1/include/c++/7.3.0/tr1/stdio.h
/usr/local/Cellar/gcc/7.3.0_1/lib/gcc/7/gcc/x86_64-apple-darwin17.3.0/7.3.0/include/ssp/stdio.h
/usr/local/Cellar/gcc@7/7.3.0/include/c++/7.3.0/tr1/stdio.h
/usr/local/Cellar/gcc@7/7.3.0/lib/gcc/7/gcc/x86_64-apple-darwin17.5.0/7.3.0/include/ssp/stdio.h
/usr/local/Cellar/gcc@7/7.3.0/lib/gcc/7/gcc/x86_64-apple-darwin17.5.0/7.3.0/include-fixed/stdio.h
/usr/local/include/c++/8.2.0/tr1/stdio.h
/usr/local/lib/gcc/8/gcc/x86_64-apple-darwin17.7.0/8.2.0/include/ssp/stdio.h
/usr/local/lib/gcc/8/gcc/x86_64-apple-darwin17.7.0/8.2.0/include-fixed/stdio.h
(Those are not Apple's headers, but GCC / GLIBC).
Using dtruss I can see that Apple clang uses the one in CommandLineTools/SDKs:
$ sudo dtruss -f sudo -u $USER clang test.c -o test 2>&1
3781/0x51d8: pread(0x3, "#include <stdio.h>\n\nint main(void)\n{\n printf(\"Hello, world\\n\");\n return 0;\n}\n\0", 0x4F, 0x0) = 79 0
3781/0x51d8: __pthread_sigmask(0x3, 0x7FFEE3A7E768, 0x7FFEE3A7E76C) = 0 0
3781/0x51d8: close(0x3) = 0 0
3781/0x51d8: __pthread_sigmask(0x3, 0x7FFEE3A7E76C, 0x0) = 0 0
3781/0x51d8: open("/usr/local/include/stdio.h\0", 0x1000000, 0x1A) = -1 Err#2
3781/0x51d8: open("/Library/Developer/CommandLineTools/usr/lib/clang/10.0.0/include/stdio.h\0", 0x1000000, 0x48) = -1 Err#2
3781/0x51d8: open("/Library/Developer/CommandLineTools/usr/include/stdio.h\0", 0x1000000, 0x37) = -1 Err#2
3781/0x51d8: open("/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/stdio.h\0", 0x1000000, 0x47) = 3 0