"Number of patches found is zero. How do I download and apply these patches? "
You must have a valid Support Agreement ID (SAID) for Data Protector, and, from this, you can create a HP Passport account that is linked to this SAID. If you don't have HP Passport, I can't find a line to apply for a HP Passport, but, when you connect to the site shown below, you will be prompted for one, with an additional choice to REgister
Once you have a HP Passport, you can use this site:
https://softwaresupport.hp.com/
You will be signing in with your HP Passport. Once signed in, select teh Product Data Protector by clicking on the Radio button. Then, you will enter your version of DP, and the OS-type you need patches for, and will be given a list of patches on the left. Expand the list by slick on the square box, as you click in each patch, you will get a patch description which include s link to download the patch
The Core patch always gets installed forst