Could any of your children have a genetic disorder if you are a carrier of the gene?

Depends. If you have a disorder that is controlled by a dominant gene, statistically half your offspring could get it. Babies don't always follow statistics, all your babies could get your dominant gene & the condition or none could & none get the condition. If you carry a recessive gene you would have no affected kids unless you had them with a carrier. Then, all or none could get it most would be carriers.
Depends. A carrier implies a recessive gene, so each of your children would have a 50% chance of having this gene. If your husband is also a carrier (recessive) then there would be a 50% chance of transmission from him resulting in a 25% chance of one of them having the disorder.