Does getting radiation, chemotherapy, and a stem cell transplant affect chances of having kids later in life?

Yes. I am not sure of your gender, but for women, usually this leads to cessation of ovulation, that may recover later. For men, sperm count may be significantly reduced, and depending on what chemo agent used, this may be permanent.
Yes. Without knowing the specifics, the regimen you describe most likely would result in infertility. That being said, men can bank their sperm before treatment, and egg preservation for women is now possible.