I have a friend who went to yeshiva and told me that after about half a year of very intensive study, he started feeling sensations throughout his body like being on drugs. At first it happened only during certain parts of the prayers, and later also with no connection to prayer at all. I also understood from things he said that there are other things he feels too, and various "spiritual experiences." How does the Rabbi explain this? He doesn’t seem mentally ill or anything like that. On the contrary, he’s a very rational guy, grounded, connected to the earth, to the world, to reality.

See the book "From the Paths of Ascent" by Rabbi Yaakov Ades.
Of course, one can argue that the brain is flexible and that the experience is in the head, but at the end of the day it is real, even if subjective.

This is what is called guided imagination. A person convinces himself that there is something special in the religious ritual, and then experiences it.
There are thousands of similar documented cases among Christians, such as Joseph of Cupertino, about whom there is testimony that he levitated. In the East there are also many similar cases, and among Muslims too there are groups that claim similar experiences.

From my experience, most people do not usually have such experiences. But sometimes religious ceremonies can arouse that kind of feeling.

There are also studies that showed a connection between temporal-lobe epilepsy and religious experiences. There are also studies that claim that the religious experience originates in guided imagination and self-hypnosis.

There is a very powerful faculty in our psyche called the "imaginative faculty," and most of the sensations people experience are imagination.
It is worthwhile to study carefully Maimonides' introduction to tractate Avot, and also The Guide of the Perplexed in several places where our Rabbi elaborates on this faculty.