Are brain fog and tremor, nervous breakdowns, difficulty swallowing and difficulty saying some words ALL symptoms of thyroid dysfunction?

Brain fog? Sorry: "Brain fog" and "nervous breakdowns" are of no use in assessing your problem because they don't really mean anything except to you. Have you been diagnosed with thyroid dysfunction? Or are you looking for some physical cause for what is actually a psychological problem?
Probably not, but. Discuss this w/ your provider. The doctor who diagnosed you thyroid disease is the best one to talk about expected effects and cautions that lead elsewhere. They'll refer you to the right specialist for things not related to thyroid. I hope you get this under some management. Best!