Can't enter into recovery mode or internet recovery erased data through disk management

Your model cannot do an Internet Recovery. You can try booting from the Recovery HD by first using Option boot:

Boot Using OPTION key

1. Restart the computer.
2. Immediately, at or before the chime press and hold down the "OPTION" key.
3. Release the key when the Boot Manager screen appears.
4. Select the disk icon for the Recovery HD, if one appears..
5. Click on the arrow button under the drive icon.

Once in Recovery Mode, you can try the following:

1. Select Disk Utility from the Utility Menu and click on the Continue button..
2. After Disk Utility loads select the drive (out-dented entry with the mfgr.'s ID and size) from the side list. 
3. Click on the Partition button in Disk Utility's main window toolbar. 
4. Set the number of partitions to one (1) from the Partition Scheme drop-down menu.
5. Set the Format type to Mac OS Extended (Journaled.)
6. Click on the Erase button.
7. Quit Disk Utility after the process is completed, and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.

If you cannot do any of the above, then you will need the two Software Restore DVDs that came from the factory.

Then there's nothing more I can help you with. You will need access to another Mac in order to get anything done. Furthermore, you will need the Software Restore DVDs that came with the computer. I suggest you make an appointment at the Apple Genius Bar for service after the stores re-open. If you need to find an Apple Store - Find a Store - Apple. Also, see How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD). You may also get Apple authorized service at a local Best Buy or contact Apple Support for more options. As long as you don't need parts, they may be able to get the computer loaded with a working OS.

Contacting Apple Customer and Support Service

1. Apple Store Customer Service at 1-800-676-2775 or visit online Help for more information.
2. If you just purchased the product, then you get 90 days of free telephone support from the date of purchase of your Apple device.
3. Primary support help at Contact Support.
4. To contact product and tech support:  Contacting Apple for support and service including international calling numbers.

Do you have the El Capitan full Installer app? If you do, then you should be able to make a bootable installer. However, because of the model you have, El Capitan will require Snow Leopard 10.6.6 or Lion to install. Here's how a bootable flash drive is made:

Bootable USB Installers for OS X Mavericks and Later

First, review this introductory article: Create a bootable installer for macOS. Second, read this How To outline for creating a bootable macOS installer. Simply use the Terminal command by copying and pasting the command line for the version of macOS from the list below. You will need an 8GB or larger USB flash drive that has been partitioned and formatted for use with OS X as well as an installer for the desired macOS version that you have previously downloaded from the App Store.

Drive Partition and Format

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the drive (out-dented entry with the w/type and size info) from the side list.
3. Click on the Erase button in the Disk Utility toolbar. Name the drive, "MyVolume". <---- IMPORTANT!
4. In the drop down panel set the partition scheme to GUID. Set the Format type to Mac OS Extended (Journaled.)
5. Click on the Apply button and wait for the Done button to activate. When it does click on it.
6. Quit Disk Utility.

Create Installer

Open the Terminal in the Utilities' folder. Choose the appropriate command line (begins with "sudo") depending upon what OS X installer you want. Paste that entire command line from below at the Terminal's prompt:

Command for macOS Catalina:

sudo /Applications/Install\ macOS\ Catalina.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Command for macOS Mojave:

sudo /Applications/Install\ macOS\ Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

*Command for macOS High Sierra:

sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Command for macOS Sierra:

sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ macOS\ Sierra.app

Command for El Capitan:

sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app

Command for Yosemite:

sudo /Applications/Install\ OS\ X\ Yosemite.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ Yosemite.app

Command for Mavericks:

sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ Mavericks.app

Press RETURN. You will be asked for your admin password. It will not echo to the Terminal window. Then press RETURN again. Wait for the return of the Terminal prompt signifying the process has completed. It takes quite some time to finish. Be patient.

The bootable installer can be used to install the selected version of macOS. Shut the computer down. Insert your flash drive into a USB port. Start the computer like so:

Boot Using OPTION key

1. Restart the computer.
2. Immediately after the chime press and hold down the  "OPTION" key.
3. Release the key when the Boot Manager screen appears.
4. Select the disk icon for the USB flash drive.
5. Click on the arrow button under the disk icon.