This pretty much sum up what I want to explain...
Basically, you need to register to council tax exemption ONLINE.
Then, bring the proof of your name (passport and BRP for international student) and address (letter from the university) to the Manchester City Council. I went there with the whole family.
Once we were there, I registered as a member of Manchester Central Library (you know I love library) and I printed school application forms for my sons. I filled in the details on the spot and seal it properly in an envelope. Then, I put it inside the mailbox at the the city council counter. No postage stamp required.
1. whether I am eligible for council tax exemption / reduction - I received it a week later - I am exempted :) (or else I need to pay more than GBP500 per month)
2. school placement for my kids.