Is a lymph node in the throat curable with an operation?

Possibly: It is hard to know without knowing the origin of the tumor/cancer. The biopsy is likely to find out what is going on and determine what the best treatment strategy will be. It could still be an infection. If cancer, further workup may be required, and plans may be made for a combination of further surgery, radiation and/or chemotherapy depending on what is going on. Surgery is the first step!

Depends: Depends why do you have enlarged lymph node: infection, metastatic cancer, lymphoma. Infection can be treated with antibiotics, cancer will require biopsy or excision and treatment depending on the type of cancer. Talk to your doctor who will give detailed answer.