Does hamartoma look like a tumor?

Yes. The word "tumor" just means growth. So, it includes benign and malignant growths as well as hamartomas. If this was a breast sample, a breast hamartoma, would look like a mass or tumor on mammography and on gross inspection of the specimen. However, once it is reviewed under the microscope, then it is known to be a hamartoma. You will note "oma" at the end which is the root of the word tumor.
Absolutely yes. In fact that's how they are found -- as a tumor someplace where there's not supposed to be a lump. Fortunately, the majority are benign and are curable.