I am studying the psyche in order to fulfill the commandment of saving lives, with God’s help (to help people suffering from depression and the like get out of their miserable state). Seemingly there is some commandment here. Is this not a fulfillment of the commandment “love your neighbor as yourself” or “walk in His ways,” or part of the commandment of Torah study, since learning this wisdom will presumably enable me to understand things in the Torah that I could not have known without this knowledge?

I will say again: the connection to a commandment, assuming there is one, is very indirect. See the breakfast example in my previous comment.
The question whether this is part of the commandment of Torah study is my uncertainty here (mainly because of my skeptical attitude toward psychology). But you need to examine whether you are really studying it for its own sake or for the diploma. Would you study this in the study hall even if you were not currently in academic studies in this field? If so, perhaps there is room to be lenient. As I said, I am inclined to think it is forbidden.

The instrumental argument too (that the study will help you understand parts of the Torah) is problematic in my opinion. In that way, there would be nothing one could not study in the study hall. Almost any field can help you understand something in the Torah: agronomy, mathematics, physics, and anything else. In my view, permission exists only if the field is important in itself, and not as a tool for understanding this topic or that. Otherwise it is only preparation for a commandment.

According to the Rabbi, is it permissible to study philosophy books? Even if, say, the author is a heretic and perhaps even excommunicated? (I am currently studying Spinoza…)

If it helps you formulate a worldview, and if in your opinion there is no prohibition in the very act of studying them (as I believe), then it would seem permissible. To me this is no different from The Guide for the Perplexed or the Kuzari. They are all “Torah in the person” (search here on the site for the definition of that).

What defines this as “Torah in the person”? Why not argue that philosophy, like perhaps psychology and mathematics, is legitimate study but not Torah? I tend to feel that it is Torah, all the more so when they are actually talking about God. The question is whether moral philosophy (and maybe even political philosophy) is considered “Torah in the person.”

It is hard to justify it here. But if studying The Guide for the Perplexed, or the aggadic teachings of the Sages, or the Maharal is Torah, I do not see what the difference is compared to studying other philosophy or psychology books, so long as it helps form a Torah worldview.
All study is legitimate. I do not know what “legitimate study” means.

Good morning. Sorry if I am writing nonsense. It seems to me, in my humble opinion, that things are being reversed here. Light is being called darkness and sweet bitter. The overwhelming majority of Scripture, and even most of the Five Books of the Torah, is not halakhic. It is more similar to the aggadic teachings of the Sages. Someone who studies the beginning of tractate Berakhot is dealing with the external act of reciting the Shema. But with the Shema itself — listening to His words, loving Him, and so on — he is not dealing. So the essence of Torah is attentiveness to His will, in love and awe, and the halakhic part is important but external and secondary. I have not innovated anything; this is what the Ramchal writes in the introduction to Mesillat Yesharim. Seemingly, on that basis, philosophy and psychology are the very pinnacle of Torah — except that in my humble opinion this is not correct, but I have already gone on too long. Wishing you success today, and the main thing is to go straight and simply.