The effective interest rate (EIR) is the annual equivalent rate. So, for example, 7% EIR would imply a quarterly rate qr = (1 + 0.07)^(1/4) - 1 = 1.70585 % and an AIR nominal rate compounded quarterly of 4 qr = 4*0.0170585 = 6.82341%. Hence
EIR = (1 + AIR/n)^n - 1 = (1 + 0.0682341/4)^4 - 1 = 0.07
However, converting between AIR and EIR does not appear to ...
I haven't verified your calculation. Generally the bank doesn't give you the calculation on rate change. They generically would mention x additional payment needed.
The last EMI would be deducted for residual amount. If you are paying by cheque, it will be refunded