How accurate are fn biopsies for thyroid? Had x2 complex cysts checked. Both came back normal. Mom had thyroid cancer. Still nervous.

Generally accurate. Fine needle biopsies are generally, but not 100%, accurate. There is a gene test called affirma, that can by done at the same time as a thyroid biopsy and can improve the accuracy of the diagnosis. There are also blood tests (thyroglobulin) which can increase in some thyroid cancers. Check w/your endocrinologist.
Thyroid nodules. Are common, malignancy rare. There are hereditary medullary carcinoma syndromes (men2), but follicular and medullary are more common. Radioactice scans can discern hot or cold nodules, but fna's and these can miss cancer.
Very. Complex cysts are seldom cancer and if they are not growing and two needle biopsies are okay I would not be concerned. You also have a right to see your pathology report; it won't be "normal" ("no pathology") if the pathologist who needled it felt a cyst, but will contain a benign diagnosis. Glad you are taking a proactive approach to your health.