Kirchhoff's junction law represents the conservation of which physical quantity?

Consider the following statements regarding the network shown in the figure.
$(1)$ The equivalent resistance of the network between points $A$ and $B$ is independent of the value of $G$.
$(2)$ The equivalent resistance of the network between points $A$ and $B$ is $\frac{4}{3} R$.
$(3)$ The current through $G$ is zero.
Which of the above statements is/are true?

Five resistors,each of resistance $R$,are arranged as shown in the figure. $A$ battery of voltage $V$ is connected between points $A$ and $B$. Find the current flowing through the branch $AFCEB$.

The current through the $1 \Omega$ resistance in the following circuit is (in $A$)

$A$ Wheatstone bridge is initially at room temperature and all arms of the bridge have the same value of resistance $(R_1=R_2=R_3=R_4=R)$. When $R_3$ is heated to some temperature,its resistance value increases by $10 \%$. The potential difference $(V_a - V_b)$ (after $R_3$ is heated) is . . . . . . $V$. Given the total voltage is $40 \text{ V}$.

For the circuit shown in the figure,the current $I$ will be .......$A$.