Starlink yes, but the standard wifi package for YC is the Browse, not the Stream, so it is good but you will not have the most unrestricted package.
No wristbands.
There is shade in the bar/buffet area of the pool deck.
Stores tend to be closed in port to avoid local sales tax issues, some bars may not open if there are a lot of people off the ship and the speciality venues do not tend to open for lunch either, but the YC restaurant will be open at lunch time as usual.