if everything is caused by material causation, then there is no room left for a ‘reason’ to cause something. The event is already fully explained in terms of the laws of nature. Where the question of 'being convinced' arises?
'Being convinced' describes a certain type of physical process in the brain.
With a mechanical causation of consciousness, the unity of self, memory, and competence for reasoning cannot be explained.
I disagree. They can be explained, but their nature isn't what is usually thought. the unity of self, for example, is a sense that is processed in the brain. It can happen that such processing fails and people can lose a 'sense of self'. It can happen that the processing identifying our bodies as ours can fail and it can happen that they are seen as foreign.
The competence for reasoning *is* limited. As a math professor, it is very clear that logical thinking is hard for the vast majority of people. But, it is *possible* to learn and to train at it. The fact that we evolved to survive means we have at least an approximation that functions for human-sized phenomena. That is the lead-in to further understanding.
Memory, from what we can tell, is produced by increased connections and easier activation of neurons. The specific mechanisms (and the possibility that there is more than one mechanism, depending on location in the brain) is still being actively researched.
It seems to me that you are unaware of a LOT of modern research that does explain these types of things mechanistically.