Single conductor connecting two parts of a circuit vs two separate circuits
The connection might be necessary. See 2)

There is no voltage difference between A and B because they are connected with an ideal wire. In some cases it is important to maintain the same reference voltage in two or more parts of a system, so we connect them together with an ideal wire. This ideal wire is often called &quot;ground&quot;.

This schematic is an ideal model of a circuit, so the dependent sources &quot;know&quot; what is controlling them because you marked it on the schematic. In the real world there would be some physical connection between the two.