How is a lymph of the neck surgically removed? are there any long term side effects in the long run? what type of anesthesia is used for a 5yr old?

I assume you mean a lymph node. In a 5byear old removal would be done asleep under general anesthesia, usually gas, after early sedation by IV drugs. (They don't usually understand/tolerate a local) A troublesome note would be easily located and separated from its connecting lymph vessels and nearby tissues. The node would then be sent to the lab for any needed tests,

The reason for the biopsy would be helpful information. Was a test for infection and CBC, Differential performed? An image guided biopsy with a fine needle should be discussed as an option. Pathology tissue diagnosis is often effective in determining the condition.