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I’m just curious what a multi-room use for a house means 

If it’s one multi-use room, it’s one space surrounded by sides made of concrete blocks, bamboo, mud, cardboard, plastic tarps, etc.  Within that space, all living activity occurs—for example, eating, sleeping, conversation and relaxation, homework, TV viewing, anything one would do in their home.  Some daily activities might occur outside those walls, ie cooking, laundry, bathing, eliminating.  The bed if there is one, and there may only be one, is in there, and it might double as a place to sit, eat, do homework, etc.  Any additional furniture would be inside the walls, and storage could be inside or outside those walls.  The one multi use room may be free standing or it could be part of a larger building.  Within the urban Kolkata setting where your sponsored child lives it is likely a room in a large old multi-story building.  Once upon a time, when CI assisted the children and families with their basic needs, sponsors got a very good feel for what destitute children and families actually deal with on a daily basis, through their articles and photos but I can see how it would now be somewhat obscure for sponsors to envision.  

More to think about:
The single room home could be as small as 3x3 meters, as in Bawana, Delhi.
Extended family sharing the space could number up to 10, or even more.
Privacy must be limited, if it exists.
Frequently we hear of a chronically ill family member who would be cared for in the space, placing additional strain on the useage of the home.

It's one room. Basically a single room home .The ones I've visited in India are mud. They had two rooms actually, though each family lived in one side. For instance one side was my sponsored kid's family and the other was a grandmother. They have one large, high bed platform with a hard cotton filled mattress. They usually have plastic chairs on the porch. There's some amount of shelving for storage. Windows have light curtains and often there's no physical door. Cooking was done in an open outside area over a fire.

My child lives in Kolkata as well and she has a cot for a bed. How should I envision that?

A cot doesn’t sound too bad. It may be a folding bed. Many sponsored children in India sleep on mats or even on the floor. You could always ask CI to check if your child would benefit from a different type of bed. I’d do this especially for a teenager.