What is this transport aircraft, and why does it sometimes cary an air data boom when the Soviet Buran Space Shuttle is on top of it?
The only aircraft that ever had a shuttle on top of them is NASA's modified Boeing 747 and Russia's Myasishchev and the Antonov 225. All of them were subsonic.

The one in the picture is the high wing 6 engine Antonov 225.

The air data boom is likely to gather data for test flights for the shuttle. Subsonic craft will affect the air in front of them (that's why you can hear them coming) so putting the sensor on a boom will help put the sensors in clean air.