a.) J.K. Roling was a single mother, and she lived in a small apartment.
b.) J.K. Roling was a single mother, living in a small apartment.
c.)Living in a small apartment, J.K. Roling was a single mother.
Can I rewrite a. into b. and c. to make a. = b. = c.?
In principle, yes you can. Be aware though that c) carries the connotation in English to native speakers that she was a single mother BECAUSE she lived in a small apartment. Also, there should be no comma in a) and b), and it's 'J. K. ROWLING'.