LSE accommodation and Intercollegiate Halls

1. Can I have two options of booking a room in one LSE hall and a room in an Intercollegiate hall? I have yet to know where to stay so may I confirm this at a later date? I mean can I apply for a catered single room (not ensuite - £218.40 - £246.75 p/wk) at Passfield Hall and catered en suite single room (£221.73 p/wk) Lilian Penson Hall via University of London?

2. Is there a link to apply for a room at the Intercollegiate Hall of Connaught Hall? If it has been fully booked, can I apply for a room in the waiting list from 2nd September and what are the chances of me getting a room in this hall?

3. I have waited for 48 hours since I firmed LSE (I chose LSE around 11pm 29/5) but I still could not book accommodation via LSE. Could you please help me with this please?