How to know if a mac is under DEP (Device Enrollment Program)?
Have you seen Apple's DEP FAQ? It says 


  Which devices can be enrolled in DEP?
  
  Any Apple Mac or iOS devices purchased on or after March 1, 2011 can
  be enrolled in DEP. Mac or iOS devices purchased from participating
  Apple Authorized resellers or carriers must be added to your DEP
  instance to be included. All iOS devices must use iOS 7 or later, and
  all Mac computers must have OS X Mavericks v10.9 or later. Once
  configured, automatic enrollment in MDM occurs at the time of device
  activation if a profile has been assigned. If a device has already
  been deployed (activated), you can trigger automatic MDM enrollment by
  erasing and restoring the device.



what are the consequences of allowing DEP, and is it reversible?



  DEP supervises and enrolls the device into your Meraki MDM. Any
  configuration profiles are going to come from Meraki, not DEP. If
  there are configuration profiles that you want to remove, make the
  change in Meraki... either remove the device from the "Clients in
  scope" list under the profile, or remove the profile completely from >Meraki (if you don't want it on any device).
  
  DEP allows for the changing of the following: App Lock (Single App Mode)
  
  Global HTTP Proxy
  
  Activation Lock Bypass
  
  Autonomous Single App Mode
  
  Web Content Filter
  
  Set background &amp; lock screen
  
  Silent App Push
  
  Always-On VPN
  
  Allow managed app installation exclusively
  
  Additionally, you can block/disallow:
  
  iBookstore
  
  iMessages
  
  Game center
  
  AirDrop
  
  AirPlay
  
  Host pairing
  
  Cloud Sync
  
  Spotlight internet results
  
  Handoff
  
  Erase
  
  Restrictions UI
  
  Installation of configuration profiles by UI
  
  News
  
  Keyboard shortcuts
  
  Passcode modifications
  
  Device name changes
  
  Wallpaper changes
  
  Automatic app downloads
  
  Changes to enterprise app trust
  
  Apple Music
  
  Mail Drop



how to contact the person who has DEP and ask them to remove it from the program?



  The line under "add to enrollment" will tell you who is running the
  DEP. You may see details by clicking add, and it will bring up
  preferences. Under this, you may read (in plaintext) who is trying to
  enroll you, and you may find out who it is.



When buying a new mac, how to know if it's on DEP? (the most important question)



  Reset it. See if it bypasses Setup. 



Someone on IRC said that if i was unable to authorize my machine from itunes then the machine is on DEP.. is this correct?



  Yes. It would bypass this under MDM or under a DEP. 



The same person on IRC says that there could be a previous owner, and this owner can format my computer and see all of my files even if i have my own icloud on it, is this correct?



  This is true. 
  
  The Device Enrollment Program enables IT to easily leverage the
  advanced capabilities of supervision without the need to physically
  tether a device to a master computer running Apple Configurator –
  supervision can be turned on with the click of a button OTA. IT also
  benefits from the avoided risks associated with unmanaged devices.
  With the Device Enrollment Program, IT can leverage un-removable MDM
  profiles and even require devices to re-enroll after being wiped or
  reset.


Best of Luck!