user-1: How can the term "spirit" be translated into Buddhist doctrine? If I may just copy paste the definition:

Moreover, could be mean anything unconditioned, permanent, or in some way separate from the rest of 'us'? The tags are clues, but I'm not being facetious.

user10100: It is citta (mind), which have cetasika (citta+nika;mind factors), such as feeling, emotions, etc. See more information in cittanupassanasatipatthana in mahasatipatthanasutta.
But if you mention to the ghost (citta+cetasikas+rupas), it is bhuta or sambhavesi in KN. Khuddakapatha ratanasutta & it's atthakatha.
Abhidhamma describe this topic as tons.

user254: Trying to translate "the seat of emotions", and looking at Ayatana, I guess the answer might be "mana" or mind -- because the "mind" is to "mental objects" what the "eye" is to "visible objects" -- in that way the "mind" might be called the "seat" of "mental objects" (which I think include "emotions").
See also:

What is the difference between Vijñāna, Manas and Citta?
A dictionary definition of mano & mana(s)

Or the answer might be "citta" (according to this extract from the definition of mano):

As regards the relation of manas to citta, it may be stated that citta is more substantial (as indicated by translation “heart”), more elemental as the seat of emotion, whereas manas is the finer element, a subtler feeling or thinking as such. 

Asking for a translation of "the soul" though, into Buddhist terminology, is difficult: because in Christianity the "soul" (or "spirit") is understood to be eternal, whereas Buddhism denies there is such a thing. I think that the word for the "permanent soul" denied by Buddhism is atta (Pali) or atman (Sanskrit) -- which I think that just means "self". In Hinduism that word is imbued with extra meaning ("the Self"), in Buddhism it's used as a simple, conventional or grammatical reflexive pronoun.
Instead of atta another possibility is "satta".

a living being, creature, a sentient & rational being, a person

A disadvantage of this translation is that "a being" isn't exclusively non-physical -- also, that in suttas like Vajira Sutta (SN 5.10) the view that there even is "a being" is condemned ... instead there are only "the aggregates".
So the "aggregates" ("khandhas") might be a good translation -- except that there are four non-form aggregates where perhaps you were looking for a single word -- and except that I'm not sure that "perception" ("sanna") for example is the "seat of emotion", and I think instead it's the various transient emotions themselves (perhaps without positing the existence of "a seat").

Incidentally the etymological origin of the word "spirit" comes from a Latin word related to "breath" or "breathing" -- that's a bit of an interesting connection, given the Buddhist practice of "watching the breath" ("anapanasati"), partly to understand how breath is connected to emotion. It's said that a meditator 'should watch the breath, in the same way that a hunter might watch an animal's lair' ... i.e. knowing that sooner or later the animal will return to its lair. In that way maybe "the breath" might be regarded as "the seat" -- I'm not sure though whether you'd count that (the breath) as "physical" or "non-physical".

-1: <p>How can the term "spirit" be translated into Buddhist doctrine? If I may just copy paste the definition:</p>

<p><a href="https://i.stack.imgur.com/OjLSq.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/OjLSq.png" alt="enter image description here"></a></p>

<p>Moreover, could be mean anything unconditioned, permanent, or in some way separate from the rest of 'us'? The tags are clues, but I'm not being facetious.</p>
 10100: <p>It is citta (mind), which have cetasika (citta+nika;mind factors), such as feeling, emotions, etc. See more information in cittanupassanasatipatthana in mahasatipatthanasutta.</p>

<p>But if you mention to the ghost (citta+cetasikas+rupas), it is bhuta or sambhavesi in KN. Khuddakapatha ratanasutta &amp; it's atthakatha.</p>

<p>Abhidhamma describe this topic as tons.</p>
 254: <p>Trying to translate "the seat of emotions", and looking at <a href="https://en.wikipedia.org/wiki/Ayatana" rel="nofollow noreferrer">Ayatana</a>, I guess the answer might be "<em>mana</em>" or mind -- because the "mind" is to "mental objects" what the "eye" is to "visible objects" -- in that way the "mind" might be called the "seat" of "mental objects" (which I think include "emotions").</p>

<p>See also:</p>

<ul>
<li><a href="https://buddhism.stackexchange.com/q/1435/254">What is the difference between Vij&#241;āna, Manas and Citta?</a></li>
<li>A dictionary definition of <a href="https://suttacentral.net/define/mano" rel="nofollow noreferrer">mano &amp; mana(s)</a></li>
</ul>

<p>Or the answer might be "<em>citta</em>" (according to this extract from the definition of <em>mano</em>):</p>

<blockquote>
  <p>As regards the relation of <em>manas</em> to <em>citta</em>, it may be stated that citta is more substantial (as indicated by translation “heart”), more elemental as the seat of <em>emotion</em>, whereas manas is the finer element, a subtler feeling or thinking as such. </p>
</blockquote>

<p>Asking for a translation of "the soul" though, into Buddhist terminology, is difficult: because in Christianity the "soul" (or "spirit") is understood to be eternal, whereas Buddhism denies there is such a thing. I think that the word for the "permanent soul" denied by Buddhism is <em>atta</em> (Pali) or <em>atman</em> (Sanskrit) -- which I think that just means "self". In Hinduism that word is imbued with extra meaning ("the Self"), in Buddhism it's used as a simple, conventional or grammatical reflexive pronoun.</p>

<p>Instead of <em>atta</em> another possibility is "<em><a href="https://suttacentral.net/define/satta" rel="nofollow noreferrer">satta</a></em>".</p>

<blockquote>
  <p>a living being, creature, a sentient &amp; rational being, a person</p>
</blockquote>

<p>A disadvantage of this translation is that "a being" isn't exclusively non-physical -- also, that in suttas like <a href="https://www.accesstoinsight.org/tipitaka/sn/sn05/sn05.010.bodh.html" rel="nofollow noreferrer">Vajira Sutta (SN 5.10)</a> the view that there even is "a being" is condemned ... instead there are only "the aggregates".</p>

<p>So the "aggregates" ("<em><a href="https://en.wikipedia.org/wiki/Skandha" rel="nofollow noreferrer">khandhas</a></em>") might be a good translation -- except that there are four non-form aggregates where perhaps you were looking for a single word -- and except that I'm not sure that "perception" ("<em>sanna</em>") for example is the "seat of emotion", and I think instead it's the various transient emotions themselves (perhaps without positing the existence of "a seat").</p>

<hr>

<p>Incidentally the etymological origin of the word "spirit" comes from a Latin word related to "breath" or "breathing" -- that's a bit of an interesting connection, given the Buddhist practice of "watching the breath" ("<em>anapanasati</em>"), partly to understand how breath is connected to emotion. It's said that a meditator 'should watch the breath, in the same way that a hunter might watch an animal's lair' ... i.e. knowing that sooner or later the animal will return to its lair. In that way maybe "the breath" might be regarded as "the seat" -- I'm not sure though whether you'd count that (the breath) as "physical" or "non-physical".</p>
