ANSWER:

You cannot offer your prayers sitting without a legitimate reason as standing up in the standing position in salah is a pillar, without which your Salah is invalid.

She can can sit on a chair for doing sujood. She should pray standing and do the ruku normally and when she has to make sujood she should sit on the chair and bend a little while keeping her hands on her knees or thighs. 

My mom has artheritis. So she cannot sit on the ground. But she can stand and she can sit and prostrate for sujood on a flat elevated surface. Is it correct to be seated on the chair for the whole salah without standing?. Is this method of sujood that she does correct?