You need to clarify further because I already answered that question. God is love, and God loves within the Trinity. It's no different than "God loves you": The Father loves the Son and the Spirit, the Son loves the Father and the Spirit, the Spirit loves the Father and the Son. But God's love is not narcissistic. So if you need further clarification than that, you need to specify it further here.

If I ask "does god love me?" I also do not need to specify that question further to get answers - why would I need to specify it further here?

You haven't answered my question. What do you mean by "love themselves"? I've already explained that God is love, and love within the Trinity is necessary. I've already explained that God is not narcissistic—excessively preoccupied with His own needs, and certainly not at the expense of others. Neither of those seemed to satisfy you, so you need to explain what you mean by "love themselves," since pure love and narcissistic self-love weren't in your wheelhouse. What do you mean by love themselves? Your reluctance to answer makes me suspicious that you're just playing some kind of game, but I'm giving you the benefit of the doubt and politely requesting that you give further explanation.

If I'd ask the question "does god love me?" Everyone would just say "yes" - and in the same way I ask "does that one person of the trinity love him/her/themselves?" And I ask that question for each of the three persons individually.

What do you mean by "love themselves"? What are you getting at? Please explain what you mean by "love themselves".

So, there is this trinity ok. If you pick any of these three persons of this trinity and look at that person individually, would the answer to the question "does that person love themselves?" be yes or no?

It's a very strange question and oddly worded, so you'll need to explain what you mean by it.

Do the persons of the trinity love themselves as well?

Just for the record, "trinitarian," not "Trinidadian". Maybe that was an autocorrect problem.

To address your question, I'll quote from Joe Boot: "If God is not the triune Lord revealed in Jesus Christ, then the doctrine of creation is rendered impossible, and man is part of a cosmic chain of being. This is because a monadic conception of God as some kind of singularity leaves us with the emptiness and void of non-personality as ultimate reality. If there is no plurality within God’s being, then there is no subject-object relationship, no particularity, but instead only a blank unity. In such a view of God there can be no foundation for knowledge, love, morality, or ethics. Indeed, without an absolute personality, there is no diversity or distinction basic to reality at all; ultimate reality is a bare unity about which nothing may be said. This is why the Trinity is so important in tackling the philosophical problem of the one and the many."

In other words, it is necessary that God is a plurality. If we deny that, we deny absolute personality. Since God is necessarily a plurality, it is therefore necessary that God's nature of love is expressed between the persons of the Trinity. The Father and the Son and the Spirit love each other. In your manner of speaking, it is necessary that God loves Himself.

But if you mean in some kind of irrational or selfish narcissistic self-love, no, God is not involved in or guilty of that. God does not have an excessive preoccupation with Hiss own needs, and certainly not at the expense of others.

'in a subject/object Trinidadian understanding, yes'? Not sure I understand what exactly you mean by that