AL Phy ~Current change in transformer

When the load resistance R decreases, the processes taking place are as follows:
--- i2 increases (using the same symbols as in the question)
--- magnetic flux in the transformer core decreases (because of Lenz Law)
--- E1 decreases (since E1 is the back emf in the primary coil)
--- i1 increases (because the supplied voltage V is constant, refer to your equation (1))
--- mangetic flux in the core increases
--- E1 increases to its original value

It is true that the ratio of E1:E2 remains almost constant and is related to the turn-ratio.

You should also be aware that in your equation (1), the potential drop across the primary coil, (i1).(r1) and the back emf E1 are not in phase. Hence, the two terms cannot be viewed as adding together arithematically.
Thus for a constant V, i1 can increases with E1 (the back emf) keeping more or less constant just by a change of the phase angle between (i1).(r1) and E1.

You should have some conceptual misunderstanding in the power consumtion in secondary coil.

please take a look in http://en.wikipedia.org/wiki/Transformer

for power, current and resistance relation in secondary coil.