Can standing near the microwave give me cancer?

No. I am not aware of any such link. You should make sure your microwave oven has a good seal on its door and is running properly.
It's different type. Microwave is different from xray. The wavelength is longer and it is non ionizing meaning it does not have the same interaction with cells as compare to ionizing radiation (xray, gamma rays). Thus, it does not have the same carcinogenic effect as xray.
As you already know, Microwavees cause heat, and while the heat penetrates, and warms your pre-ready food, it does not ionize, or knock an electron off a critical molecule at the nuclear level. It will cook the cell before it cause genetic damage. The "wave" interefered with older pacemakers, ; not sure about the new ones.