No.
It not designed for use by any under the early teens at all and most of the health sensors are calibrated for adults.
It would be better to use any one of the numerous purpose built newborn vitals monitors. They’re available from multiple stores and sites.
The original SE would be borderline. It’s viable now but it likely won’t see watchOS 11. However the SE2 would be a perfectly viable choice. Most people don’t need blood oxygen, ECG and wrist temp tends. You can also replicate a good bit of Double Tap with Quick Actions and a good Hand Gestures set up.
Well that’s new.
Those all appear to be apps that can receive videos, same for the list that showed up for me just now. So I would imagine that you have the option to save to photos or start a post/message with one of the other apps or attach the video as a file to a submission form.
One of my options is “My Verizon - Diagnostics.”