Can a mammogram show whether a lump is benign or not?

No. A mammogram shows characteristics of a lump that make it more likely to be benign or malignant. The mammogram is given a bi-rads score of 0 to 6. A score of 3 is indeterminate, and 4 is suspicious for cancer. The only way to know absolutely is to have a biopsy. This site gives more info about bi-rads: http://www.Breast-cancer.Ca/screening/bi-rads.Htm.
Sometimes. Some masses have specific characteristics on mammo that enable the radiologist to make the diagnosis of a benign lesion, without biopsy. These include: hamartoma, oil cyst, calcified fibroadenoma, fat necrosis, lymph node, calcified cyst. For most other lumps, further imaging, follow up, or biopsy are likely needed.
Not always. When reading a mammogram the radiologist categorizes the findings on the mammogram based on the degree of suspicion from 1 to 5, with 5 being highly suspicious for malignancy and 1being negative. The only definive way to know a lump is benign or malignant is a biopsy. But not all lumps need a biopsy such as simple cysts. Ultrasound can be helpful. Please see your physician if you have a lump.