addressing the points you raised one at a time.
Babies are sick with teething and colds and any number of sniffles at any point in time. From all reports I have read, I have seen no reports of fever, lethargy, or anything to indicate she was "reallly" sick (as in should be at home on bedrest, death's door sick). I have not seen any reports that the ailment was anything more than minor or that it was contagious.
I never stopped our lives each time any of my children were slightly ill with the sniffles or teething. I guess we parent differently.
I think any family gathering with a camera there would generate lots of photos of lots of the children with varied cousins, grandparents, etc. We are only being shown select photos from this party. Photos that feature baby Lisa.
I have seen nothing to indicate that they were the only photos taken. I assumed that the photos of others at the party were not published to protect the minor children and other relatives who are only involved in this case by the accident of familial relation.