how do I download apps on Mac OS High Sierra 10.13.6

You can download them from the App Store app as explained in the support document you posted from, as long as they are compatible with high sierra, or you can get them directly from the developers website again as long as they have a compatible version for High Sierra.

Any specific issue you are having?

A couple I'd recommend...

A more modern/safer browser...

Might try this, it's Chrome Browser without google & without Ads...

https://brave.com/

Look into the Free LibreOffice, it handles MS Office files like Word & Excel, & Page Layout…

https://www.libreoffice.org/

I would like to Download a compatible version of Keynote from Apple Computer for MacBook Pro running os 10.6.

If you're running Snow Leopard  see if you can find a copy of iWork '09 on ebay.

yes, am facing this issue whereby am been asked to keep restarting the application in the process of installing the high Sierra on my MacBook early 2011 13inch