Yes. If one parent has thalassemia minor, and the other parent has normal hemoglobin (not a carrier of Alpha thal, beta thal, sickle cell, etc...), then the children of the two parents will be normal (have normal hemoglobin), or close to normal (have thal minor). Thal minor generally doesn't cause symptoms. In rare cases, a new or additional mutation could occur and make the situation more complicated.
Yes. Don't forget, you are normal too - thal minor has very little effect on an individual's health. If your husband is negative for thalassemia trait, the children will either be negative, or at worst with thal-minor, in which case the biggest thing to worry about is having kids with another thal-minor person as the children of two thal-minor parents may be quite seriously ill.
Yes. Your children will likely be normal, however if your husband is heterozygous for thalassemia (meaning he carries one disease gene and one not) there is a 25% chance your child will be affected and a 50% chance they will be a carrier. Carriers for thalassemia (thalassemia minor) generally are asymptomatic and do not need treatment.