Absolutely, as long as the parents respected and supported the child’s choice to enter. If the parents were against the child’s entry into the service, it is highly innapropriate.
I don’t see why not. Maybe that person is extremely proud of his or her uniform and they are hoping that their parent has gone to heaven and can see them in their uniform. We really never know what’s going on in a child’s head, give them a bit of space and don’t pick on them for what they decided to wear. They lost a parent or parents and it’s not right for someone to question what they chose to wear. Instead of questioning them, why not try being there for them as they are going to need lots of love and understanding.
It may vary from culture to culture. In Britain military uniform is acceptable just about anywhere for any occasion.
Further Further Point
The child may not have any other formal clothing for such an occasion and really the child is perhaps doing what they think would most honor their parent’s memory. If the Child has not yet graduated from basic training they may be required to wear that particular uniform.