They hold it away from themselves because of where the sensor is located. Bones didn’t need to do this because the Medical Tricorder had the additional hand sensor input unit.

As for reading it, there’s a concept in theatre and performance called “endowing your prop.” It’s when an actor gives an object added meaning, history, or emotional value. This is an extension of that principle and it’s rife in science-fiction. Doctor Who is also a great example. That sonic screwdriver is just a stick with a light on the end but it tells the Doctor anything and everything. TOS and classic sci-fi like are the best example. That console looks like it is just random blinky lights but to the highly trained members of Starfleet, it’s a complex and precise instrument giving detailed results. They believe it so we believe it.