yes

They did. It is part of the resvinet scoring symptom. but unlike adults who can tell you how they feel, if their cough is improving, shortness of breath, how congested they are, etc these signs are just not very sensitive on their own. fevers can come and go for example

Antiviral therapy works better the earlier you start treatment, so testing adults early in the course of illness gives you the best chance for seeing a treatment effect. ONce you are in the hospital you have probably been sick much longer. so not stupid at all. what would have happened if pfizer onlly tested paxlovid in hospitalized patients (where it failed), and not outpatients (where it was successful)

It might be easier to tease out a treatment effect in peds too in the outpatient setting (one component in resvenit is medical intervention - if you are already hospitalized probably already on oxygen, antipyretics, etc)