Opening a new window in order to copy files from another window overtakes the other window; both windows cannot easily be seen at the same time
New windows will shift down and over a slight bit. Hasn't changed in over 30 years. You can set the Finder to open in Tabs (Settings > General). I don't think that would help, much.
I use Spring-loaded folders which pretty much eliminates the need for any more than one Finder window. You can enable it in Accessibility System Settings, Pointer Control, Mouse & Trackpad. You can adjust the time it takes to spring open the folder. I keep "starting point" folders in the Sidebar so I can easily get to common locations.
Drag an item over a folder and it will spring open. You can continue to drill into where you want to drop. If you set the delay to a longer value, it won't open too fast. If you then want to speed it up, the spacebar will spring it open immediately.
Alt-tab doesn't tab between open windows, but between applications
Alt-tab does nothing on a Mac. Cmd-tab cycles between open applications.
Cmd-` cycles between open document windows in an application.
Ctrl-tab and Shift-ctrl-tab go to next/previous tab in most applications.
Delete key doesn't work when multiple files are selected.
What do you want the Delete key to do with a file? It should do nothing on its own.
Cmd-Delete will move selected items to the Trash. Opt-Cmd-Delete will delete immediately.