I think they have installed some paid software on your device!
I have used one in the past from round about that time. It was called eBlaster and it recorded everything - every single keystroke typed, sites that were accessed, people communicated with. Couldn't believe the amount of data you could obtain about any system.
What happens is - they'd need physical access to the system, download it from a link or usb and sync it to an email address where they will receive screenshots of activity and they can set the frequency.
The programme run in stealth mode unless you tell it not to.
I just used it to prank my bro but this is horrible.
Try these things:
Use activity monitor to assess what apps/files are consuming resources.
Then go to finder and find the files for the app and press cmd+shift+. and it will show you all the hidden files and folders for any directory.
Even if nothing looks suspicious in acitivty monitor still do the above check all home folders, root directories etc.
If you get a name that sound suspicious - google it (from another computer otherwise they will get a red alert) if its one of these spyware companies then you can get the police involved.
What country is this?