I just wanted to know if I can hook up an directv box to my laptop and use my laptop as a tv

Yes, if your laptop has the appropriate audio and video inputs needed to connect the DTV receiver. A video capture card as outlined above would work or some laptops have native hdmi inputs. Another solution is to connect a sling box to the DTV receiver. You can then watch on the laptop with the sling box app.

There is no mobile app for laptops, some have downloaded an android emulator called Nox from bignox.com.

You would need a video capture card with the appropriate video and audio inputs to use your laptop as a TV.  Not recommended.