When was the first modern air-air refueling? By modern I mean
"compatible with a modern tanker/receiver (either boom or hose)".

This question seems to be tricky, in that many of the early systems
would not be compatible with a modern airplane.

For bonus points, when was the first carrier based refueling done?
Both the tanker and receiver must be carrier based, but the buddy
system works.

-Charles Talleyrand