How was the wedding day? Can the groom get married on his birthday?

Yes, as long as your's birthday is not the anniversary of his death, marriage is an important event in life, and it will only happen once in a lifetime, so be careful. But I still think it's better and more formal for you to invite your parents to dinner together. You can check the birth dates of both parents online to see which day is more suitable. I think it's better not to call my parents, because marriage is a matter for two families, and parents' opinions are also very important. May you live happily all your lives!