The surface under grass of grass courts is slower or faster than hard courts/clay courts? What about its uniformity (i have read that it is compacted soil, but it does not seems that uniform)? References are welcomed.
The surface under grass of grass courts is same if not faster than hard courts, which will ultimately be faster than clay courts.
From WIMBLEDON website article:
The soil must be hard and dry to allow 13 days of play without damage to the court sub-surface.
To achieve the required surface of even consistency and hardness, the courts are rolled and covered to keep them dry and firm. Regular measurements are taken to monitor this.
After the change of grass to 100% Perennial Ryegrass (since 2001) the difference between grass court and other types has reduced significantly. Worn-down grass will behaves more like a hard court as the soil under is more like concrete, with a higher coefficient of friction.(source)
From answer of Loring Chien to question at Quora:
The dirt has little texture like asphalt or laykold courts. So its very hard and the ball tends to skid making it a "fast" court, even faster than hard courts.
As for uniformity, yes it is compacted soil but the ground under the grass is never as perfectly level as hard court is, so there are always places that will cause the ball to bounce unpredictably(source). So it does not seems uniform, but with the level of work that goes into maintainig the court only small patches will appear in different parts of court. Those patches can produce irregular bounces — obvious to the player, but barely perceptible to fans in the crowd or television viewers.(source)
From a Forbes article:
“The bad bounces are gone, the courts are now so level, the preparation of the grass-court is so immaculate that it is now behaving exactly like a hard court,” Craig O'Shannessy Strategy analyst for Wimbledon, Australian Open, ATP World Tour, Infosys, NY Times & Tennishead.
The answer I have given is mostly based on Wimbledon grass court but should be same for other court.