Will the cancer spread to other parts of my body?

We hope not. What makes a cancer "evil" is the ability of cancer cells to travel outside of the organ where they arose and take over another organ; this is how cancer can be life-threatening. In advanced cases of cancer, we can identify these "invaders", but most often, these cells are present but undetectable. The stage of the cancer gives us an estimate of this probability, leading to the rec for chemorx.
Probably. If left untreated, many kinds of cancer develop a capacity to spread to other parts of your body. Fortunately, there are many types of treatment that are designed to prevent or delay this from happening. There is so much variety in how cancers behave; talk to your doctor to see about your type.