1... You are right that most cases of hypothyroidism
are due to HASHIMOTOS THYROIDITIS
2.. Confirmation is done by doing the test for THYROID PEROXIDADE ANTIBODIES
3.. You do require the treatment with synthetic thyroxine
and generally it is needed for lifelong.
4..As far as your cholesterol is concerned ,you should start taking lifestyle measures like doing regular exercises and taking more of green vegetables and fresh fruits.Reduce your weight.avoid junk foods.
Goal is to reduce your total cholesterol
below 180,reduce you LDL to below 100 and triglycerides to below 150.
There is no need to start anti cholesterol medicines as regular exercises and correction of hypothyroidism should make you all right.