Is it possible to have a partial nephrectomy?

Yes. In some cases a partial is recommended and in some cases it is not possible, even when that is the initial plan. Surgery does not always go as planned.
Yes. Depending on the size and location of the kidney mass, a partial removal of the kidney cancer is a very good option to help preserve the remaining good kidney tissue. This has in fact become the mainstay of treatment for many tumors and the long-term data shows good cancer control with partial removal versus removing the entire kidney, which was the traditional type of surgery in the past.