Hello,
Sorry to hear you are having issues. You can not scroll the Start menu in the pinned shortcut area while in Windows 7/Modern style. What you can do is add more space for shortcuts or use the Grid mode. You can scroll when you in "All Program" mode.
From what I know, you can not remove Start menu button. But, I believe, you could Hide Start menu button, by using transparent custom Start button. Something like this: https://www.wincustomize.com/explore/start_menu_buttons/565/
Thank you,
Basj,
Stardock Community Assistant.