So just a simple question.
How exactly is shelter calculated?
What are the aspects that count for it?
Is it having a bed to sleep in and chair/table to eat at? Do comfy beds and comfy chairs count for more?
Are buildings needed? Do buildings need to have a roof?
Yes.
Yes.
If you want a better score! 
It’s not a building without a roof. 
I seem to be able to get a shelter score of 5+ with only two buildings (default shared sleeping quarters, and default dining hall). Since my food score is almost always 9+, this is enough to get me 7+ on the town, which I can live with. (especially since I usually have a sub-0.5 shelter score by the time the first building is done…)
Does a Cave count as shelter?