Do I need to format Macbook Pro md101hn/a? Yesterday I bought a used macbook pro from a person.
Though I have removed that users account from laptop and erased home directory too.

Now I have 2 questions related to it as below.

Do I need to format the disk?
Any tools to measure performance of the laptop?
Nuke &amp; Pave.

This should really have been done by the previous owner. Basic security precaution. If a bad actor had hold of this machine, half his life would now be in their hands.

You don't want anything inherited from the previous owner - good or bad.
The possibility you inherited a virus etc are very very small, but at the moment, all the Apps on there &amp; even the OS itself still belong to the previous owner &amp; you would need their Apple ID log &amp; pass to update anything at all.

So, go for a clean start.
Wire up to your ethernet if at all possible; WiFi if you really can't, but avoid any WiFi that uses a Portal structure, that will not work.


  
  Start up from Internet Recovery by holding down   Cmd ⌘   Opt ⌥   R  immediately after turning on or
  restarting your Mac. Release the keys when you see the Apple logo.
  Startup is complete when you see the utilities window.
  Open Disk Utility from the utilities window, then use Disk Utility to erase your built-in hard disk using the Mac OS Extended (Journaled)
  format. Quit Disk Utility when done.
  Choose Reinstall macOS (or Reinstall OS X) from the utilities window, then follow the onscreen instructions. This installs the
  system that came with your Mac when it was new. It isn't associated
  with your Apple ID, so the new owner can use the App Store to upgrade
  to a later version using their Apple ID.
  


Source: Apple KB - How to reinstall macOS - If you're selling or giving away your Mac

Don't do Step 4 from that page, proceed as the new owner &amp; set it up using your own credentials.