Hi,
Include paths are intended for header files only.
If you have external library you can add the path into linker:

In case of any other file/object:

This is how the settings above influence the .arg file used by makefile:
"./Project_Settings/Startup_Code/system_S32K144.o"
"./Project_Settings/Startup_Code/startup_S32K144.o"
"./Project_Settings/Startup_Code/startup.o"
"./src/main.o"
-L:My_External_lib.a
-T
"C:/Users/r200040/workspaceS32DS.ARM_1.3/S32K144_Segger_test/Project_Settings/Linker_Files/S32K1xx_flash.ld"
-Wl,-Map,"S32K144_Segger_test.map"
-Xlinker
--gc-sections
-mcpu=cortex-m4
-mthumb
-specs=ewl_c9x_noio.specs
--sysroot="C:/NXP/S32DS_ARM_v1.3/S32DS/arm_ewl2"
"Any_other_file.bin"
-lc:\MyLib
Regarding the elf question please have a look here:
https://community.nxp.com/docs/DOC-332252
Hope it helps.
Stan