I have an iPhone 4, and one of their recent updates added an 'always online' feature, where the user can receive messages even if Skype isn't open on their device.

Lately I've been using Skype on my desktop PC, and any message sent to me also appears on my iPhone, and it gets a bit annoying after a while.
Skype for iPhone has no settings, and I've turned off all notifications for Skype in the iOS notification centre, but however I still get notifications of the messages that I receive on Skype.

I've looked briefly for a solution to this, but I can't find anything specific to my usage case.
Two questions:

* Can Skype notifications for new messages be switched off on my iPhone- Switching all notifications off for Skype does not do anything.
* Is it possible to stop it from showing me as Online all the time? It's inconvenient because I recieve business messages when I'm trying to sleep, and I require to be contactable 24/7 so I can be contacted by my customers if they have a fault with their gameserver (I offer gameserver hosting)- but being able to IM me 24/7 isn't what I want.