Cannot Download Additional Components for OSX (El Capitan)

Do not attempt restoring macOS unless you are connected to the AC charger or have a fully charged battery. I assume your MBA is able to do Internet Recovery:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

If possible back up your files before proceeding.

1. Restart the computer. Immediately after the chime hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

Note:

1. To install the version of OS X that was currently installed use Command-Option-R.

2. To install the original factory version when the computer was new use Command-Option-Shift-R.

You can only downgrade either by re-downloading the El Capitan full installer or erasing the disk and restoring your El Capitan backup. To do the former you will need to erase the drive and install macOS from the original disks that came with the computer when it was new or by using Internet Restore if your computer came with macOS pre-installed and with no installation disks. Here is the latter:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

If possible back up your files before proceeding.

1. Restart the computer. Immediately after the chime hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

Note:

1. To install the version of OS X that was currently installed use Command-Option-R.

2. To install the original factory version when the computer was new use Command-Option-Shift-R.