1. When opening QAP, at the bottom I would like a filter field that takes you directly to the program I'm interested in running;
Something like the Quick Launch go box? "Quick Launch" under the "Tools" menu or press Shift + Ctrl + Q.
2. In the programs menu, when accessing the program I want to run, I can, with the right mouse button, open a menu with options, such as "paste the program path to the clipboard".
Right clicking in a Windows popup menu is not technically feasible. But what you describe exists using the Alternative menu. See:
https://www.quickaccesspopup.com/what-ar...-features/