How to identify the reason for connecting the root partition in read-only mode?

Question

linux

Greetings.

On one of the virtual machines on the host (VMware ESXi 6.5), the root directory is mounted in readonly mode. I went through all the error logs, no errors. I try to do mount -o remount,rw / nothing happens.
When you try to perform any actions related to writing to the disk, an error occurs No space left on device.
I forgot to indicate that there is definitely space on the disk. Only 40% of the space is occupied.
deployer @ app ➜ ~ df -h
Filesystem Size Used Avail Use% Mounted on
udev 3.9G 0 3.9G 0% /dev
tmpfs 799M 8.9M 790M 2% /run
/dev/sda1 118G 48G 65G 43% /
tmpfs 3.9G 0 3.9 G 0% /dev/shm
tmpfs 5.0M 0 5.0M 0% /run/lock
tmpfs 3.9G 0 3.9G 0% /sys/fs/cgroup
tmpfs 799M 0 799M 0% /run/user/1000

Answer 1

No space left on device

What is not clear to you here? Add places.

Answer 2

and conclusion df -i.

Answer 3

Try fsck, don't you?