Connection between Arduino and Mission Planner

One possible solution is to connect the Arduino to one of the Pixhawk’s telemetry ports (UART) and then the Pixhawk can forward the data to your ground station.

The Arduino would need to transmit the data in MAVLink format to the Pixhawk (there’s a tutorial here: MAVLink and Arduino: step by step).

No. You would need to build that functionality yourself.

A receiver is not necessary, but highly recommended - especially if a manual takeover is required.