The patient described above is likely suffering from Graves disease (a common presentation of hyperthyroidism). Along with the excessive stimulation of thyroid epithelial cells, in Graves disease there is lymphocytic infiltration in the retro-orbital region. Lymphocytic stimulation of adipocytes and fibroblasts are responsible for the development of exophthalmos.
Graves disease is an autoimmune disease whereby there is self-recognition of thyroid receptors. Antibody binding to these receptors leads to the excessive release of thyroid hormones, causing symptoms of hyperthyroidism, including: diaphoresis, heat intolerance, tachycardia, increased basal metabolic rate (weight loss), fatigue, and tremors. Although traditional antithyroid medications do not affect Graves-related ophthalmopathy, glucocorticoids are effective in controlling exophthalmos by decreasing inflammation and thereby reducing extraocular volume.
Reid et al. review the diagnosis and treatment of hyperthyroidism: "The most common cause of hyperthyroidism is Graves disease. Other common causes include thyroiditis, toxic multinodular goiter, toxic adenomas, and side effects of certain medications. The diagnostic workup begins with a thyroid-stimulating hormone level test. When test results are uncertain, measuring radionuclide uptake helps distinguish among possible causes."
Hatton and Rubin explain that "cytokine release, [leads to] proliferation of fibroblasts, increased deposition of extracellular matrix, and adipocyte differentiation and proliferation." They note that this results in "edema, enlargement of the extraocular muscles, and increased volume of the orbital soft tissues occur with ensuing exophthalmos."
Answer 1 and 2: Anti-thyroglobulin antibodies would be more consistent with Hashimoto thyroiditis.
Answer 3: Decreased levels of T4/T3 is more consistent with hypothyroidism.
Answer 5: Anti-myelin antibodies would be more consistent with multiple sclerosis.
Hatton MP, Rubin PA. The pathophysiology of thyroid-associated ophthalmopathy. Ophthalmol Clin North Am. 2002 Mar;15(1)
Reid JR, Wheeler SF. Hyperthyroidism: diagnosis and treatment. Am Fam
PMID:12064074 (Link to Abstract)