HOW DO I CHECK INK LEVELSON MY COMPUTER FOR THE PHOTOSMART 6520

First of all it is not recommended to do any hardware troubleshooting from your end, because if your HP Photosmart 6520 is within warranty so that would be voided by company. So after that you have to pay further for any of the issues related with hardware which might have lay off if you may have not touched the Printer. It is suggested to check if your printer is under warranty from the link given below:
http://support.hp.com/us-en/checkwarranty

You can also directly contact 'HP Support Center' from the link given below for further assistance:
http://h20566.www2.hp.com/portal/site/hpsc/public/help/contactHP/home

GuruAid.com

HP recommends that you use genuine HP ink or toner supplies. HP cannot guarantee the quality or reliability of non-HP or refilled cartridges. If you do not use genuine HP cartridges, the steps in this document might not resolve print quality issues.
Low ink can contribute to poor print quality. Follow these steps to check the ink levels, and then replace any low or empty ink cartridges.


http://support.hp.com/in-en/document/c03954004

you can find the standard procedure here

change the black ink cartridge

you don't! you scan pages one by one

Try going to the maintenance screen and running the cleaner and any other adjustments that can be made from there.

In Windows, go to Devices and Printers. Right-click on your printer. Select Printing Preferences. Select Color. Select Print in Grayscale and Black Print Cartridge Only. Select Ok.

The printhead on a 6520 is not removable.

It is not removable on the 6520.