The updated EasyTether 1.0 should fix the "Smartphone side requested connection shutdown" problem.
The updated version can be downloaded for free from Android Market.
As for the notification icon, unfortunately this ongoing notification (well, the underlying
mechanics) is the only way to protect against a very aggressive built-in
task killer (the common reason for connection drops) in the latest
Android OS versions. This feature solved many customers' issues with the "Connection dropped" message.
To remove the icon, slide-down, touch "Select to disable", then uncheck the USB setting in the EasyTether screen. Don't forget to check it again when you'll need the app.