I want to add iOS application to the dock - but I can't find the application to add it

You'll be able to find all Apps already installed on your iPad and iPhone using the App Library.

To access the App Library page, simply swipe to the left from your Home Screens; the last page is the App Library. Here you will find both automatically curated App groups, an alphabetical list of installed Apps - and a Search tool. Apps can be re-added to your Home Screens - from which an App can be simply dragged to the Home Screen Dock.

More information about using the App Library can be found in the respective User Guides:

Find your apps in App Library on iPad - Apple Support

DnD? Do Not Disturb? Download?

I have absolutely no clue as to what you may continue to be causing difficulties.

All Apps are visible within the App Library. From here, as detailed within the iPad User Guide, Apps can be added to one or more Home Screens. From the Home Screen, Apps can be dragged to the Dock - although the total number of Apps that can be added to the Dock is ultimately limited by the iPad screen size.

For a 12.9" iPad Pro, the maximum number of Apps that can be added to the dock is 16 - in addition to which an additional 3 recently used App icons can appear to the right of the Dock divider (of which one may be the App Library icon). Other iPad models, with smaller screens, will accommodate fewer App icons within the Dock.

Widgets themselves are limited to any Home Screen - or the slide-out Today view that can be summoned from the left-edge of the first Home Screen. Widgets can't be added to the Dock.