If my mammogram is normal and I feel a lump, does that mean that it isn't cancer?

No. A screening mammogram is designed to find cancers that are not palpable; while effective, it can miss 10-15% of breast cancers. If you have a palpable lump, then you need a diagnostic mammogram & ultrasound which will focus in on this lump. Even if these tests are normal, I recommend that you see a breast surgeon for a formal exam, just to be on the safe side.
No. If you have a palpable lump that is new or changed over time you should have that evaluated with breast ultrasound or diagnostic mammogram and possibly biopsied. A negative screening mammogram should not be relied on if a lesion is present.
No, mammography. Is only about 80% sensitive for detecting cancers, so 20% will not be seen. Your lump needs to be completely evaluated. Ultrasound would likely be the next step. Biopsy could also be possible. Discuss with your doc.