How can I turn off Skype's notification of "is online", which is visible to other online members when log in?
Is it possible to do that at all?
If you would prefer to hide your presence status completely, you can change this in your profile settings to make yourself invisible.
Tap your profile picture > Tap the Settings button > Tap Privacy > then you can toggle Show my presence to others on or off.
EDIT: The above setting no longer exists.
You can't. You can control only your notifications.
A way to avoid being displayed as "online" by others is to get in skype "invisble" or stay in skype constantly with a status of your choice.