Is a woman who suffers from waswas (obsessive doubts/whispers) considered sinful if she succumbs to the intrusive thoughts of the khawaswis (whisperers/devils) and says "I am a disbeliever" to get rid of them? And is ritual bathing (ghusl) required of her? And must she continue to perform ablution (wudu) and prayer (salat) despite the doubts that plague her?

There is no cure for obsessive whispers (waswas) except to ignore them and turn away from them, giving them no attention. This requires strength of will and sincere determination. So, do not pay attention to the waswas, no matter how great or numerous it becomes. If Satan whispers to you that you have disbelieved, do not care, and be firm in your conviction that you are upon Islam. If he whispers to you regarding ablution or prayer, pay no attention and continue with what you are doing, and seek refuge with Allah from Satan. You may also consult the advice section on the website or a trusted doctor.