Can someone take your picture on your computer by accessing it somehow?

It depends;

If they use Remote Desktop Connection (or simaliar), they can access the camera software,

If they hack files, then no, unless the photo has been taken,

If they hack a social network site, no,

If they use livestream on YouTube, yes.

No, if you dont have a webcam,

If you do, then they can, but it is easy to stop them - as you can deny them Remote access.