Oftentimes cats with hyperthyroidism have trouble with not using the litter box because they produce a lot more poop more frequently. That is why she was doing it before the meds started - she had the hyperthyroidism (HT) but was just not diagnosed yet. This was a sign she was giving you that something wasn't right. The pooping stopped when the HT was starting to be controlled.
It is a known side effect of the Tapazole for some cats to tear up themselves around their head and face. Unfortunately she was one of them. The dose she is on now may not be sufficient to control the hyperthyroidism, but this will show on the follow-up blood tests. It may take some time for things to normalize if that dose is an adequate one for her. One thing that may help is to feed a very highly digestible diet that won't leave as much for waste. Also digestive enzymes and probiotics may help. Until she is controlled with the meds, you may want to keep her in one room of the house to prevent accidents. If she cannot tolerate the Tapazole at a level that is controlling her HT, you may want to consider radio-iodine therapy, which is a one-time curative treatment.
http://www.radiocat.com/section4.html
Holistic Wellness Care