>1-With my head spinning, I fell on the bed.
>2-I fell on the bed, with my head spinning.
>Can’t both of the above sentences mean both a and b:
>a-I fell on the bed AND my head was spinning.
>b-I fell on the bed BECAUSE my head was spinning
Yes. They can mean both “a” and “b.” They clearly mean “a,” but certainly “b” would be implied in most cases.
“B” becomes a question of logic, but in everyday speech the cause-effect relationship would probably be understood though it is not explicitly stated.
In formal writing or in a formal situation like testifying in a lawsuit, you would want to be more direct as in “b.”