“When I open regedit and expand a folder and open regedit later the folder stays expanded. How can I disable this?”

In regedit, navigate to
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Applets\Regedit

Look for the value LastKey. Double-click it and clear the string. Then right-click the Regedit key (in the left hand pane) and select Permissions. Set Permissions to Deny for any/all users/groups.