A:AnswerThe Dell Inspiron 24" Touch-Screen All-In-One (your desktop) might not be correctly receiving or recognizing the display output from the work laptop through the docking station. You could try changing the output on your device and docking station to make sure they match, or make sure all your drivers/firmware is updated.
A:AnswerYes, you can connect a third monitor. There are 3 HDMI adapters and if you should choose to use a different method other than HDMI, you can use a dock or hub to attach a third monitor.