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That's about 31 square feet. I don't think there's anybody on this board who would put more than 15 chickens into that space and that is a WHOLE BIG LOT (very very crowded) unless you live in, like, Hawaii and they will never ever want to spend time indoors except to sleep at night.
Most people feel much more comfortable with the flock dynamics at 4 sq ft per chicken or higher. At 4 sq ft per chcken, that'd be 7-8 chickens.
Personally I'm really a whole lot happier with 6-10 sq ft per chicken of indoor coop space (plus run of course), in terms of how they act -- but this is partly influenced by my being in an area where there are long stretches of the year when outdoors is not really such an appealing concept to a chicken. FWIW, at my stocking densities, your coop would hold something like 3-5 chickens.
Plus run space, of course. 'How much run space?' At least 10 sq ft per chicken but preferably a lot more, facilities and budget permitting.
Whether to close off the rafters is a personal decision, but I probably would -- just makes extra hard-to-clean mess, and prevents you from being able to use droppings boards (which I am a major fan of), and so forth.
Make sure the eaves (soffits) of the shed are very well predator proofed btw - raccoons are tremendous climbers.
Have fun,
Pat