The Duke was happy to share his general happy birthday statement to his wife with their 9+ million followers. What he actually said to her on that day, how they spent time on that day, and even what he gifted her, remains private.
The Queen owns a bulk of property that is managed by the Crown Estate. The Crown Estate is an independent real estate business that returns all of its profits to the Treasury. Per the Sovereign Grant, the Crown Estate grants the Queen 15% of the profits made from lands which the royal family has owned for centuries. Does that sound like “taxpayer’s money”?