The Benelux Royals Message Board: Princess Delphine

I saw that Princess Delphine was with the royal family for National Day. What exactly is her relationship with the Royal Family, both on a personal level and as an institution? I know how they're related, her being King Albert's daughter with Sybille De Sely Longchamps; but I'm wondering about her relationship with the individuals/institution of the royal family.

Is she considered a member of the RF just like King Albert and Queen Paola's other children? Does she often participate in official engagements with the royal family? Is she given her own official engagements/patronages as a royal?

How has she been received by the RF? Is she included in private gatherings of royal family members as a "member of the family", or is she more of a "bother" that the RF just feels they need to include in public for PR purposes but in private...not so much?

According to Wikipedia (yes, I know), her children are also HRH and Prince and Princess. Are Belgian royal titles inherited through both the male and female lines? If not, why are Delphine's children HRHs?

And, finally, what do the Belgian people think about her?

I apologize for all the questions, but her and her children's status and "integration" into the RF are all very confusing to me.