One should realize that although the principles of Daqiq al-Kalam stems from a view found in the physical nature, it should not be restricted to apply to physical entities only. For example, the Principle of Discreteness applies to physical objects including the spacetime and material structure (atomism). It also applies to social, psychological and economic problems as well, where we view the components of the system in question as discrete structure and further look at it in terms of the Jawhar (the substance) which is immutable and the Arad (the accident) which is ever-changing and non-durable. So, obviously we have to designate first what is Jawher in the system and what is Arad. The other example is the Principle of Re-Creation which applies not only to physical systems but to any other system, social, environmental, economic or else.
The basic methodology of the new kalam is to subdivide the elements of the problem in question into Jawhar and Arad and look for the factors affecting the Jawhar through the ever-changing Arad. In such a process we expect to have some uncertainty resulting from the ever-changing Arad. This uncertainty has to be taken into account for predicting the outcome of the development of the system in question.
This is a topic that has been preliminary treated in my paper entitled "re-Creation: a possible interpretation of quantum indeterminism. Adopting the principle of re-Creation allows us to understand many problems in quantum physics more clearly.
The Quantization of spacetime or at least the quantization of time is badly needed in constructing a theory of quantum gravity. You cannot quantize gravity without quantizing spacetime. If the quantization of the space can be realized through the quantized spin of particles, the quantization of time seem to be more difficult to realize.
This question can basically treated as a daqiq al-kalam problem, but it can be treated within the context of jalil al-kalam too. First the fundamental objection to Darwin's theory of biological evolution is the assumption of random mutation. Should it be random mutations we would have not seen ascending direction of evolution. Why there should be ascending evolution then. Second, kalam negates the changes happening under the assumption of natural necessity. Causal determinism is not a proven observational fact, thus we cannot say that such changes causing evolution would happen by innate nature, simply because laws of nature are indeterministic. Yes, laws of physics are deterministic but has no active authority to do actions. Laws of physics are descriptive not prescriptive.
Kalam is able to provide an alternative analysis of biological evolution and this leads to the so-called Adaptive Mutation. Details are discussed in my book Daqiq al-Kalam: the Islamic approach to Natural Philosophy.
We should always remember that the new Daqiq al-Kalam is a logic system that uses some finite number of principles to analyse other systems. This includes natural physical systems, social systems, environmental and economic systems. Such applications will be further developed in practice once the quantitative assessment system becomes available.
Here are some Articles about Kalam applications that you may download.