You need to have one of the followings documentation to prove you are the resident of the address:
1. Telephone Bill under your name
2. Gas Bill under your name
3. Electricity Bill under your name
4. Water Bill under your name
But it will be safe to call the primary what kind of document you need from the above before you do the registration. Different school require different documentation.
You are entitled to apply the school under this Net as you can claim your family like your mom who still have the name under the apartment, takes care of your kid.
I think you need to check EMB to confirm.
If you accept the seats offered by "DSS", you cannot participate the "Lucky Draw". They have Letter of Undertakings for you to sign - as my friend did to DBSPD for his son.