Can an aircraft (civilian or military) land with its brakes already engaged?
Can an aircraft land with its brakes already engaged at the max
  landing speed of that aircraft?


Yes... 

Im gong to assume that by brakes engaged you mean to full, preventing the wheels from spinning. First Lets consider the two different types of planes. Tail wheel planes will most likely nose over depending on how the plane is landed. A tricycle gear equipped plane will most likely grind through the main gear. Remember the nose gear does not generally have a brake (in my GA experience it never has a brake).  

Although I would not advise it. It depends really what you mean by "can it land" it will touch down and the tires will simply lose traction and start skidding (eventually to a stop). The results (on a dry runway) may be similar to what we saw with JetBlue flight 292 which had its nose gear turned 90 degrees. The gear was basically ground through like it was sanded down. The tires in this case will all begin to heat up severely and eventually fail. My guess would be that the skidding will vary from side to side and cause the plane to weather vane quite a bit as if differential braking were used.

You may also damage the runway quite severely.