Created programs compiled with gcc using root,now I am into problems about not having execution permission & chmod gives .o file with EXE format error - c

Question

I have simple code files and Makefile the generates some executable files. Now I am having problem with running it. First that the output of gcc is not giving me .o file with execution permission. Which is surprising, at the bottom is my makefile I ran into these issues below.
With ls -lh command it says I only have maximum read and write permission to a writeshmem.o. same for all files in the directory. Even though I don't remember setting any system wide permission for outputting .o file without execution permission from gcc. And I DO NOT REMEMBER REVOKING ROOT USER PERMISSION.
root#fawad:/home/fawad/Desktop/Shared# ls -lh
total 44K
-rw-r--r-- 1 root root 263 Sep 6 14:07 Makefile
-rw-r--r-- 1 root root 359 Sep 6 14:10 destroy_shmem.c
-rw-r--r-- 1 root root 3.9K Sep 6 14:10 destroy_shmem.o
-rw-r--r-- 1 root root 381 Sep 6 13:40 readshmem.c
-rw-r--r-- 1 root root 4.1K Sep 6 14:14 readshmem.o
-rw-r--r-- 1 root root 1014 Sep 6 11:58 shared_memory.c
-rw-r--r-- 1 root root 267 Sep 6 14:09 shared_memory.h
-rw-r--r-- 1 root root 490 Sep 6 13:30 writeshmem.c
-rw-r--r-- 1 root root 4.2K Sep 6 14:14 writeshmem.o
As u can see there is no execution x
After above when I gave permission with
root#fawad:/home/fawad/Desktop/Shared# chmod +rwx writeshmem.o
I got this error
root#fawad:/home/fawad/Desktop/Shared# ./writeshmem.o
bash: ./writeshmem.o: cannot execute binary file: Exec format error
What that above error even means. It make no sense to me how giving permission to a file messed up with the EXecution format of the file. Someone can please explain why it matters for a file to cause this error. I only change the permission.
Makefile
CC=gcc
CFLAGS=-g -Wall
OBJS=shared_memory.o
EXE=writeshmem.o readshmem.o destroy_shmem.o
all: $(EXE)
%.o: %.o $(OBJS)
$(CC) $(CFLAGS) $< $(OBJS) -o $#
%.o: %.c %.h
$(CC) $(CFLAGS) -c $< -o $#
%.o: %.c
$(CC) $(CFLAGS) -c $< -o $#
clean:
rm .o $(EXE)
Update
after reading comment(You should remove the .o from the executable names) by kaylum I removed .o from executables in makefile But I still get error
root#fawad:/home/fawad/Desktop/Shared# ./writeshmem
bash: ./writeshmem: Permission denied
and same output from ls -lh
-rw-r--r-- 1 root root 251 Sep 6 14:59 Makefile
-rw-r--r-- 1 root root 3.9K Sep 6 15:00 destroy_shmem
-rw-r--r-- 1 root root 359 Sep 6 14:10 destroy_shmem.c
-rw-r--r-- 1 root root 4.1K Sep 6 15:00 readshmem
-rw-r--r-- 1 root root 381 Sep 6 13:40 readshmem.c
-rw-r--r-- 1 root root 1014 Sep 6 11:58 shared_memory.c
-rw-r--r-- 1 root root 267 Sep 6 14:09 shared_memory.h
-rw-r--r-- 1 root root 4.2K Sep 6 15:00 writeshmem
-rw-r--r-- 1 root root 490 Sep 6 13:30 writeshmem.c
everything including writeshmem is still with only rw permission and without x