For PDF files if you want the generic PDF icon and not a copy of the file itself, you'll first need to do a File->Get Info, select the icon in the Get Info window, press Command-C on your keyboard ...

Even more annoyingly if I try to copy a .html file I've edited to a different folder, it silently copies my entire folder tree with it, overwriting whatever was there.

Choose the HTML file. Open the Bookmark manager by press Ctrl+Shift+O after opening the Google Chrome browser. Then, click the three-dotted icon, and select the Import bookmarks option.