Sometimes I transfer pictures or files from my laptop to computer and after processing them I would store them back on my laptop, this would be much easier if I can do something like described above.
So both computer and laptop would be turned on, and connected to separated monitors but somehow they would communicate like there is one computer extending on two monitors.
Yes, this is possible but requires software. Depending on how fancy you want it, it will either be not seamless or may cost money.
See a link of possible options here: https://www.pcmag.com/how-to/how-to-control-multiple-computers-with-one-keyboard-and-mouse
Microsoft's Mouse Without Borders seems to be the best choice here, but may respond a bit chunky at times: https://www.microsoft.com/en-us/download/details.aspx?id=35460
