Can teenage men get breast cancer?

No. Breast cancer is much more rare in men than women, occuring in about 1:100, 000 men. The rare man with breast cancer tends to be diagnosed at a later age than women. I am unaware of any reported case of breast cancer in a teenaged male.
Yes rarely. If you have a lump, esp if there's a family history esp of male breast ca, should be checked. Your best treatment options would involve an asps plastic surgeon.