Current flow stops at battery's positive terminal?
First, Kirchoff's Voltage Law (KVL) applies whether there's current flowing through the branches you traverse or not. In your circuit you could replace R3 with an open circuit, and replace R2 with an arbitrary network or resistors, transistors, etc., and your KVL equation would still hold: \$5\ {\rm V}+V_1+V_3=0\$. It wouldn't be much use for calculating the branch currents because you wouldn't be able to write \$V_3\$ in terms of branch currents, but it would still be a valid equation.

Second, current does flow through the battery. It doesn't flow as electron current in a metal, but as ions flowing through the battery's dielectric.