I'm currently using Linux Mint 18.3 and want to use 18.1 but on the same root file system with all the same local configurations. But when I tried to use the existing root partition while installing 18.1 in a new boot partition, it said that it would delete directories like /usr, /var, /tmp etc... I want to know what all such files I should back up so that I could have the same experience even after a new install.

what conf files have you changed personally? that'd be one type to save. as far as /usr /var/tmp not much in there worth saving in conf most are kept in /etc

you could run
to see what prints out concerning config file of all sorts. just modify the path to check specific directories for config files.

most conf files you might be worried about are in your home dir some even are dot (hidden) files.

Assuming you run as a normal user most of the time, most of the config files that affect your day-to-day experience (configuration of your desktop environment, configuration of your web browser, etc.) are going to be in your home directory.

These will mostly be hidden files (beginning with a .) so if you are backing up your home directory, be sure not to miss those! (Even if your home directory is in its own partition separate from your root partition, back it up anyway. That way if you make a mistake and format the wrong partition, you won't lose everything.)

Because you are downgrading, you will have some older software versions. There is a chance that they might not always properly read the config files produced by the newer version (options may have been added, formats may have been changed, etc.) so if you start getting error messages you may need to make some edits to your config files to make them compatible with the older software versions.

are you sure you got this the right way round?

what exactly are you doing there?
install from scratch to the same partition without erasing it first?
iirc this was possible with some installers, maybe still is.

you should probably make a complete clone of the whole drive, because afaics what you are doing there is unpredictable at best and destructive at worst.

Thank you.
I took a backup of my home in another partition and installed on the partition, that deleted all the files I wanted.
Unfortunately the backup tool didn't copy the subdirectories.
I'm marking this SOLVED.

what I do is
cp -r is recurive so it copies everything including sub dir and its contents.
mv moves everything.

Oh, thank you very much.
I'll definitely use this the next time!