In case of emergency, an aircraft may have to descend very quickly. Is there some performance (L/D ratio with full spoilers, descent rate, ...) to be proven in the certification process for such descent?
There is a descent requirement, but it's perhaps not in the way you imagine as it has to do with oxygen supply. FAR 122.333 subpart K states:
(b) Crewmembers. When operating at flight altitudes above 10,000 feet, the certificate holder shall supply enough oxygen to comply with §121.329, but not less than a two-hour supply for each flight crewmember on flight deck duty. The required two hours supply is that quantity of oxygen necessary for a constant rate of descent from the airplane's maximum certificated operating altitude to 10,000 feet in ten minutes and followed by 110 minutes at 10,000 feet. The oxygen required in the event of cabin pressurization failure by §121.337 may be included in determining the supply required for flight crewmembers on flight deck duty.
This specifies that a turbine aircraft must be able to descend from it's maximum certificated altitude to 10,000ft in 10 minutes or less. This means the maximum descent speed is variable to maximum certificated altitude, so if an aircraft's ceiling is 42000ft it must be able to descend at least 3200fpm, it it's 25000ft then 1500fpm.
As for how that's done I don't think the regulations say, it's up to the manufacturers to develop aircraft that can meet the requirement.
In addition to oxygen supplies, there are also regulations about cabin pressure. The descent rate required can be determined by the probability of decompression.
If certified to operate above 25,000 feet, cabin pressure altitude must be less than 15,000 feet "after any probable failure condition in the pressurization system."
For "any failure condition not shown to be extremely improbable:" the cabin altitude is limited to 25,000 feet for 2 minutes, and is not allowed to exceed 40,000 feet.
So for any "probable" failure, the aircraft must be able to descend to 15,000 feet before the cabin pressure is completely lost. For any failure not "extremely improbable," the aircraft must be able to descend to 25,000 feet within 2 minutes of losing all cabin pressure.
These probabilities are:
Probable: more than 10-5 (1/100,000)
Extremely improbable: less than 10-9 (1/1,000,000,000 or "not anticipated to occur during the entire operational life of all airplanes of one type")