What powers the air required for pneumatic brakes in large airliner aircraft? Is it bled from the engines, or do they have a separate motor and pump?
For a medium size turboprop, the F-27: two separate compressors, driven by the turboprop engines.
From this article
Fairchild’s F-27 is the first American-made plane to use a complete pneumatic system to operate landing gear, wheel brakes, nose wheel steering, propeller brakes, and passenger door operation. It also has an emergency air supply that will lower the landing gears and operate the brakes.
Compressed air for the system is supplied by two 2-cfm, 3300-psi compressors located in each of the engine nacelles. The compressors are driven through a gearbox by Rolls Royce Dart engines, which power the aircraft. They carry their own individual dehydration and filtration equipment to supply clean, dry air at a pressure of 3300 psi
Most present day airliners use the hydraulic system for the landing gear, including wheel braking. For instance on the B737:
The normal brake system and autobrakes are powered by hydraulic system B. If brake pressure drops below 1500psi, hydraulic system A automatically provides alternate brakes which are manual only (ie no autobrake) and the brake pressure returns to 3000psi.
The hydraulic systems are each powered by an Engine Driven Pump and an Electric Motor Driven Pump.
As far as I know, no modern airliner uses air to power the brakes. The systems are hydraulic.