I found the solution based on the discussion available at https://unix.stackexchange.com/questions/377345/installing-arm-none-eabi-gcc and the documentation available on https://mynewt.apache.org/latest/get_started/native_install/cross_tools.html#installing-the-arm-cross-toolchain.

The name and structure of the software changed over time. The arm-none-eabi-gcc is gcc-arm-none-eabi now, and so on.

$ sudo apt-get remove binutils-arm-none-eabi gcc-arm-none-eabi
$ sudo add-apt-repository ppa:team-gcc-arm-embedded/ppa
$ sudo apt-get update 
$ sudo apt-get upgrade
$ sudo apt-get install gcc-arm-none-eabi
$ sudo apt-get install gdb-arm-none-eabi 

And finally, to verify the downloads, you can run the following commands:

arm-none-eabi-gcc --version
arm-none-eabi-g++ --version
arm-none-eabi-size --version 

If i understand you correctly, a more detailed question is:
What configure options did 'GNU Arm Embedded Toolchain' developers used when building newlib libraries shipped in gcc-arm-none-eabi-6-2017-q2-update-linux.tar.bz2 archive?
These ones for newlib:

--target=arm-none-eabi --enable-newlib-io-long-long --enable-newlib-register-fini --enable-newlib-retargetable-locking --disable-newlib-supplied-syscalls --disable-nls

And these ones for newlib-nano:

--target=arm-none-eabi --enable-newlib-reent-small --disable-newlib-fvwrite-in-streamio --disable-newlib-fseek-optimization --disable-newlib-wide-orient --enable-newlib-nano-malloc --disable-newlib-unbuf-stream-opt --enable-lite-exit --enable-newlib-global-atexit --enable-newlib-nano-formatted-io --disable-nls

How I got it? Let's walk through the process:
These packages are build on launchpad, where from you find all the builds that took place on lanuchpad. I picked gcc-arm-none-eabi 6-2017q2-1 from 2017-10-24. There i can find the buildlog. I grepped the buildlog with | grep "^+ " | grep "configure " | grep 'src/newlib' and i was left with:

+ /<<PKGBUILDDIR>>/src/newlib/configure --target=arm-none-eabi --prefix=/<<PKGBUILDDIR>>/install-native --infodir=/<<PKGBUILDDIR>>/install-native/share/doc/gcc-arm-none-eabi/info --mandir=/<<PKGBUILDDIR>>/install-native/share/doc/gcc-arm-none-eabi/man --htmldir=/<<PKGBUILDDIR>>/install-native/share/doc/gcc-arm-none-eabi/html --pdfdir=/<<PKGBUILDDIR>>/install-native/share/doc/gcc-arm-none-eabi/pdf --enable-newlib-io-long-long --enable-newlib-register-fini --enable-newlib-retargetable-locking --disable-newlib-supplied-syscalls --disable-nls + /<<PKGBUILDDIR>>/src/newlib/configure --target=arm-none-eabi --prefix=/<<PKGBUILDDIR>>/build-native/target-libs --disable-newlib-supplied-syscalls --enable-newlib-reent-small --disable-newlib-fvwrite-in-streamio --disable-newlib-fseek-optimization --disable-newlib-wide-orient --enable-newlib-nano-malloc --disable-newlib-unbuf-stream-opt --enable-lite-exit --enable-newlib-global-atexit --enable-newlib-nano-formatted-io --disable-nls

A bit of Sherlock Holmes and i deduced that the second line is newlib configured to build as newlib-nano (--enable-newlib-reent-small), the first is newlib configured to build as full newlib.
To answer your topic question, to recompile newlib and newlib-nano the same way pass the options I have posted above to newlib ./configure script.

First of all, __libc_init_array() belongs inside extern "C". The map file you have above has it correct: it gets pulled in from libc_nano.a(lib_a-init.o).

This is not really the problem though. In your vector table, you have Reset_Handler where you should have the initial value of the stack pointer, and main where you should have the reset handler. main should never be in the vector, it is called by the reset handler as a normal function, not through the vector.

The crash you are having is most likely because you don't have a correct stack pointer, and the code is trying to use the stack.

Also, the first thing you do in your reset handler is call __libc_init_array. This is wrong. You need to (at least) copy the initialized data and zero the bss section first. If you are following the CMSIS pattern then you also need to call SystemInit. See the sample startup code and linker scripts in the STM32CubeF4 package.

EDIT: The above problems are in your pseudocode; the code doesn't match the pseudocode and doesn't have the above problems.

The next problem is that you have deleted half of the standard linker script. Try looking at the source of __libc_init_array to see what it needs. It needs the init array sections etc.

Here is an example with them in:

.init :
{
  KEEP (*(SORT_NONE(.init)))
}
>FLASH

.text :
{
  *(.text .text.* .stub .gnu.linkonce.t.*)
}
>FLASH

.fini :
{
  KEEP (*(SORT_NONE(.fini)))
}
>FLASH

.preinit_array :
{
  PROVIDE_HIDDEN (__preinit_array_start = .);
  KEEP (*(.preinit_array))
  PROVIDE_HIDDEN (__preinit_array_end = .);
}
>FLASH

.init_array :
{
  PROVIDE_HIDDEN (__init_array_start = .);
  KEEP (*(SORT_BY_INIT_PRIORITY(.init_array.*) SORT_BY_INIT_PRIORITY(.ctors.*)))
  KEEP (*(.init_array EXCLUDE_FILE (*crtbegin.o *crtbegin?.o *crtend.o *crtend?.o ) .ctors))
  PROVIDE_HIDDEN (__init_array_end = .);
}
>FLASH

.fini_array :
{
  PROVIDE_HIDDEN (__fini_array_start = .);
  KEEP (*(SORT_BY_INIT_PRIORITY(.fini_array.*) SORT_BY_INIT_PRIORITY(.dtors.*)))
  KEEP (*(.fini_array EXCLUDE_FILE (*crtbegin.o *crtbegin?.o *crtend.o *crtend?.o ) .dtors))
  PROVIDE_HIDDEN (__fini_array_end = .);
}
>FLASH

.ctors :
{
  KEEP (*crtbegin.o(.ctors))
  KEEP (*crtbegin?.o(.ctors))
  KEEP (*(EXCLUDE_FILE (*crtend.o *crtend?.o ) .ctors))
  KEEP (*(SORT(.ctors.*)))
  KEEP (*(.ctors))
}
>FLASH

.dtors :
{
  KEEP (*crtbegin.o(.dtors))
  KEEP (*crtbegin?.o(.dtors))
  KEEP (*(EXCLUDE_FILE (*crtend.o *crtend?.o ) .dtors))
  KEEP (*(SORT(.dtors.*)))
  KEEP (*(.dtors))
}
>FLASH