Is it possible to monitor people?
Yes, in fact, with a good enough connection, you can get real time streaming from someone's screen, but generally they won't do that, and will only do 1 frame per 5 or 10 seconds. And not only screen-monitoring, but also keylogging to steal all your usernames/passwords, and even spoofing things such as placing CP on your computer or using your comp in a ddos attack. Just a world of possibilities.
How to detect it?
You are on the right track with checking "netstat" (btw, if you want to be thorough, use "netstat -a" to show ALL connections). It essentially boils down to this: he has a way to send information to your computer and receive information from your computer somehow through the internet. If he is only receiving info from your computer and he uses UDP, then checking active connections is useless, however, if he is using TCP or is sending info to your computer through TCP or UDP, then you will find an active connection or listening port with 'netstat'.
What is most likely is that he has a two-way TCP connection started by a trojan or worm on your computer which is connected to his remote server. You must somehow find this connection and see what ip it leads you to. You can use just basic tools such as netstat to find this out, or you can use some kind of tcp/udp dumper to listen to your computer's outgoing and incoming traffic and pin point exactly how he is doing it (make sure to close any other applications which connect anywhere, even just an open webpage can intermittently send packets which will lead you off the trail). You can also simply use firewall application to track all connections and check how exactly it happens.
How to prevent it?
Think of it in very simple terms, HE HAS A VIRUS ON YOUR COMPUTER. This virus is stealthy, it only connects to his computer and performs various functions such as screen capture. REMOVE THE VIRUS, and you remove his ability to track you. Scan with your Anti-Virus, and use additional AV's such as Malware-Bytes Anti-Malware or CCleaner or maybe even ComboFix. In case you can't do that, do some manual investigation and removal (be careful not to destroy your system). If that doesn't work, blocking any untrusted communications can stop his monitoring, but it won't remove the virus.
- WallShadow <3