When someone uses Remote desktop to log on to your computer, first of all, he needs to provide credentials for an account which has permission to do so on your machine, and secondly, you'll notice, because your session will get locked. I'm not aware that it would be possible to use Remote Desktop to see what you're doing on your system. There's also Remote Assistance, which (I assume - I haven't ever used it) is similar but doesn't lock out the session, as its whole purpose is to let someone else see what you're doing or control your computer remotely while you see it.
I use TeamViewer regularly which, I assume, does it similarly to Remote Assistance. In TeamViewer, you'll notice that someone has joined remotely your session, as a window informing you about it appears on the desktop. I assume all legit remote access application do so, exactly so that they won't get misused.
Malicious applications, on the other hand, surely won't inform you. And in Windows, an application doesn't need admin privileges to be able to take a snapshot of the screen. If you cannot trust your coworkers not to install malicious software on your office computer, then I'd suggest not to use sensitive applications on it. And definitely move to two factor authentications for all important applications (at the very lest, e-banking as well as email - hijacking someone's email is often enough for an identity theft).
Regarding Skype, it has been demonstrated to harvest URLs, usernames and passwords sent via its chat system, at least since Microsoft acquired it. But if you don't use it to send sensitive information, I wouldn't be too afraid of it. If it contained malicious software, someone would already notice - Microsoft is under close public scrutiny (otherwise its password harvesting wouldn't become known).
In case you are using Dynamic IP, then its quite difficult.
Reboot your system.
In case of windows, start the Task Manager and have a look at the running processes. It can give your some idea which all softwares are running state.
In case of malicious activity try to kill the process but at your own risk.