Hey mate,
Firstly I would recommend removing the network services suggested in the screenshot - ie. no SSH or FTP.
Then:
-View logs (the more the better) for around thing time you think this may have happened.
-Once we track it down the removal should be easy enough.
Now we fix the bigger issue of how they got in.
-For this we update all plugins, themes etc. as well as removing any you absolutely don't require.
The Instragram problem has be stumped at the moment but with some more info I might be able to help.
We also shouldn't rule out the unlikely possibility that your device is the issue but we can cross that bridge when/if we come to it.
I do this stuff for work all the time so I'm confident I can help.