The doctors are sending it off for genetic testing to determine whether it is benign or not. If it comes back benign, they will probably recommend waiting and watching to see if it grows or changes in appearance. If it comes back still suspicious, they will probably recommend a partial thyroidectomy (one thyroid lobe removed) or full thyroidectomy (entire thyroid removed). If it comes back malignant, they will want to remove the whole thyroid.
If it is suspicious for neoplasm with Hurthle cell involvement, the biopsy is "indeterminant" because it is impossible to tell by biopsy whether it is benign or not (just based on what the cells look like). Before genetic testing, they would recommend thyroid surgery (partial or full thyroidectomy), but with genetic testing they can sometimes tell if it is benign, and spare many people without thyroid cancer from unnecessary surgery and a lifetime of needing thyroid medication. Sometimes, even if it is benign, they still won't be able to tell by genetic testing and still might recommend surgery, so if the genetic test comes back as suspicious and they recommend surgery, it doesn't mean for sure you have thyroid cancer.
I'm going to share what happened to me since it is similar to you, but please know it is impossible to know if you have thyroid cancer at this point (and you might not know even after the genetic testing, which is what happened to me). And then I'll try to tackle your biopsy results in detail.
I had a thyroid nodule that was suspicious for neoplasm (with Hurthle cells), I believe I was told there was 33% risk for malignancy after the biopsy, which is similar to the risk you were given. We sent it off for Afirma genetic testing, and it came back as still suspicious (~50% risk for malignancy). At this point I was scheduled for a hemithyroidectomy (one thyroid lobe with the suspicious nodule was removed), which happened 2 months after I got the Afirma results. I was convinced I was one of the many people with a Hurthle cell neoplasm where the genetic test came back suspicious but it was benign. In my case, it actually was cancer, and I had to go back and get the second lobe removed (I also had 2 more nodules that were cancerous). I was lucky and we caught the cancer(s) early enough that I did not need radioactive iodine treatment.
I have Hashimoto's (an autoimmune disease that attacks the thyroid) and the central compartment of the neck (area near the thyroid) was full of swollen lymph nodes. I think 14 total were pulled out during my two surgeries, at the second surgery 8 were pulled out in a massive clump and three were stuck to the side of the thyroid. None of the lymph nodes contained cancerous cells, it was just my immune system attacking and destroying my thyroid.
On to your biopsy:
A thyroid nodule does not mean thyroid cancer, most thyroid nodules are benign. Since you already have a biopsy of your knowledge, we know that specific nodule is at an increased risk for being cancerous due to what the cells look like under biopsy.
Lymph node - I wouldn't begin to make any assumptions about the lymph node at this point. In my case, my lymph nodes did not contain cancerous cells and there were a ton of swollen lymph nodes in my neck. What your lymph node signifies, I don't know. Thyroid nodules are more likely to be cancerous if they are more tall than wide, but as for lymph node, I doubt that rule applies, lymph nodes are not the same as thyroid nodules. (My two ultrasounds before my first surgery made zero note of swollen lymph nodes, which were clearly in there).
Suspicious for Hurthle cell neoplasm.
From Wikipedia: A Hurthle cell is a cell in the thyroid that is often associated with Hashimoto's thyroiditis as well as benign and malignant tumors (Hurthle cell adenoma and Hurthle cell carcinoma, formerly considered a subtype of follicular thyroid cancer).
If a biopsy is composed mainly of Hurtle cells, it is difficult/impossible to tell by that biopsy if the nodule is cancerous or not. This is what happened with my indeterminant biopsy and is what is happening with yours. It does not mean you have cancer, it only means that they cannot tell whether you do or not by biopsy.
Possibility of parathyroid lesion. -- We have 4 parathyroid glands, attached to the posterior (back) of the thyroid gland, they regulate calcium levels. I'm not sure exactly what they are referring to here - I doubt they mistook an accidental biopsy of the parathyroid for Hurthle cell neoplasia (I'd assume parathyroid cells look very different from Hurthle cells). Parathyroid glands can sometimes become swollen, but I have no idea what they are referring to. Possibly they aren't sure if the swollen lymph node is parathyroid and not a lymph node? (My surgeon was not sure whether the three lymph nodes attached to my thyroid were actually part of my parathyroid glands, and didn't know for sure if one of my parathyroids was removed until the pathology came back - it appears they are still in my neck, regulating my calcium levels).
Risk of malignancy etc. - that is an estimate of the percentage of people with Hurthle cell neoplasms that end up with being diagnosed with thyroid cancer or NIFTP. Since that isn't 100%, if they can differentiate between people with benign nodules with Hurthle cells versus malignant nodules, they can cut down on unnecessary thyroid cancer, and as someone without a thyroid, if I could have kept mine, I would have. Getting back to normal thyroid hormone levels has been the hardest two year struggle of my life, with lots of fatigue and not feeling like myself (I'm in a much better place now and almost normal, but the first couple years post-thyroidectomy were pretty awful). Not everyone struggles to get back to normal hormone levels, but I did. I also did not have much of a choice - my thyroid needed to come out.
I'm sorry for such a long response - in short, they can't tell by biopsy whether it is cancer and are doing the genetic test before recommending surgery (or not). It is impossible to say at this point you have thyroid cancer or not, and your risk for cancer is still below 50% (25-40%). I shared what happened to me because I had a similar first part of the experience (nodule, suspicious for neoplasm biopsy, sent off for genetic testing), but that does not mean you will have the same genetic testing result or thyroid cancer diagnosis as I did.
Good luck, and I hope all goes well for you.