Potentiometer Working
Assuming A1 and Rh are an ammeter with negligible resistance, we can ignore them.  Does seem a strange assumption since ammeters have shunt resistors in parallel, but an ammeter  has negligible resistance.  It has to be to get a valid answer to OP's question.  As the BJT said If there is a current flowing through \$R_h\$ then \$V_b\$ ≠ V. 

You also have a Galvanometer G, which essentially is an ammeter with negligible resistance.  Again ignored.


  Also, is it true that if E > V then the current will be supplied by E and not V?


Yes &amp; No.  Both sources will supply current to the circuit, but since \$R_{bA}\$ is in parallel with E (across the terminals), E is the only supplier of current to \$R_{bA}\$.  It does not matter whether E > V, E = V or E &lt; V.


  My question is that why, at point b, E has no effect on Vb?


It is how V is connected to b &amp; c.  If you look at the circuit, c = 0V, so potential across \$R_{bc}\$, \$V_{bc}\$ = V.  b &amp; c are across the terminals of V.  No resistors to drop potential.  Again, relationship between E &amp; V is irrelevant.

Not a part of the question but there are three cases:


If E > V, then \$V_{Ac}\$ is negative (relative to c).  OP question.
If E = V, then \$V_{Ac}\$ = 0 and no current flows in \$R_{bc}\$.
If E &lt; V, then \$V_{Ac}\$ is positive.


This is the only voltage which changes in the circuit.