The Specific Problem
I saw this question a couple days ago and started writing an answer, but didn't finish. When I came back to it, I reloaded the page to check if anyone else had answered and found that the question had been put on hold for being unclear. While the question is worded somewhat confusingly, I believe that understand what the OP intended to say.
The OP ostensibly describes a first-order theory of propositional logic with an additional relation "explains," written "$E$," which I would assume they have defined elsewhere. The mention of Platonism and propositions being "objects" are not strictly relevant, and likely have more to do with the context or motivation for the question than the details of the question itself. This does not affect the answer.
The OP presents two issues:
1) how can a particular natural-language expression (marked 2. in the original post) be converted to a symbolic expression in the language of their theory?
2) which statements cannot be converted to such an expression, and are there stronger logics in which such statements could be expressed?
For the first of these, the OP states:
...consider this statement:
- For any propositions x and y, if x explains y, then for any proposition z if z is true then x conjoined with z explains y.
It appears,..., we can't translate this into FOL. (sic)
The confusion seems to stem from an assumption that the statement is not expressible in FOL. This is not the case, the statement can be written as follows$^*$:
$$\forall x.\forall y.x E y\implies[\forall z.z\implies (x\land z) Ey]$$
or, using the OP's "is true" predicate:
$$\forall x.\forall y.T(x E y)\implies[\forall z.T(z)\implies T((x\land z) Ey)]$$
For the second point, the OP seems to be asking for a quick explanation of higher-order logics.
I could be wrong about my interpretation of the question, but as far as I can tell, this is what the OP meant. Assuming that my understanding of the question is correct, what should I do about it?
The General Problem
Not every question is going to be worded perfectly. SE users are human, and humans are notoriously error-prone. Maybe I'm mistaken, but it seems that some questions get closed for being unclear when in actuality they're just stated in an unconventional manner. This is especially true when the question mixes vernacular and technical language or the poster mistakingly uses one term in place of another - something which the muggles among us are especially prone to. While I don't understand every question that I come across, there are times [I hope] when I can get the 'gist' of what a user is saying and provide an appropriate response, even if the question isn't ideal.
What should I do when I think that I understand and/or have an answer to an on-hold or closed - and, more specifically, "unclear" - question?
$^*$ the use of the logical conjunction is based on the use of the word "conjoin." "conjunction" is a deverbal noun with the same root as "conjoin." The word "conjoin" corresponds to the verbal form of the root "conjungo" ("conjunctio" $\to$ "conjunction" : "conjungo" + "tio" $\to$ "conjoin" + "tion"). In context, "$x$ conjoined with $z$" most likely means "the conjunction of $x$ and $z$," referring to logical conjunction. Why the OP would use "conjoined with" instead of "and," we may never know.