I have asthma and I'm pregnant. Could my asthma affect my baby or labor/delivery?

Only if severe. Asthma can cause less oxygen for you and the fetus This is rare if the asthma is treated well and responds. Seeing a provider early in pregnancy and maintaining good control usually avoids any potential problem.
Yes/no. If your asthma is controlled, you should be fine. As you get bigger, the growing baby can push on your lungs and sometimes cause breathing to be a little worse with underlying asthma, but if you keep regular appointments with your GYN, you should be fine. Best wishes.