Thank you so much for helping me reaching near the completion this project.
Adding the external clock as per the above image, has not solved the problem, I will need to check it on a real hardware from now on. Few last questions please:
1) Please explain my earlier question, that as soon as the interrupt happens, what exactly is happening, my understanding upto now says (please correct me if I am wrong):-
a) Few registers are saved [Which takes some time - Now, I have 15 byte variables, 2 Bit variables & 4 alias for 4 port pins - How do I calculate the exact delay & come up with a value to load into timer1 so I get perfect 1 sec intervals] (my pic is also running on 32.768kHz)
b) As soon as the first instruction is executed in the ISR, does timer1 keeps the value 0 in it untill ISR is executed in full OR it starts incrementing straightaway regardless if it is in ISR or main code. The latter makes more sense to me as I think thats why you advised to reload it as a first instruction in the ISR.

Please help me find answers to the above and hence get perfect 1 sec intervals.