Say I have a formal language such that x is an individual constant and symbolically has a particular value (say 2) a proposition such as x+1=3 already has the value of true, and I cannot define a binding operation such as a quantifier on to x like ∀xP(x) as this is a badly formed sentence and has no truth value.
Then the symbols "x" and "2" are synonymous. "x" is just another way of writing "2", and the statement "x = 2" is a tautology (like "2 = 2" or "x = x"). This is not the usual convention in mathematics, but if you want to define your syntax in that way, you can do so.
Say I have a free variable x in my formal language, I can in the context where x can change to values in the domain of reals define ∀xP(x) as either being true or false.
Earlier, you told us that "x" means "2" at the level of syntax. Now you are telling us that "x" is a variable. This means that "x" has two different meanings, and the sentence "x + 1 = 3" is syntactically ambiguous - you could mean "x, the variable, plus one is three" or you could mean "two, the number, plus one is three". Normally, we try to avoid this in formal languages, because the whole point of using formal languages is to eliminate syntactic ambiguity. As a result, it is going to be very difficult to engage in formal reasoning with such an ambiguous language.
This is entirely different from the semantic notion of writing something like "let x = 2." In that context, "x" is still syntactically a variable, but we are describing the interpretation of the sentence in which the variable x takes on the value two. The variable x is a different object from the symbol "x," because the former is a semantic object, and the latter a syntactic object. This distinction between syntax and semantics is, I believe, the point of confusion in your question. Substitution is a syntactic transformation which converts a semantic interpretation back into "pure" syntax. Importantly, substitution preserves the semantic meaning of a sentence, under a given interpretation, but does not preserve its syntax, nor its semantic meaning under other interpretations.
Similarly, we must distinguish between the "∀" symbol (a syntactic object) and the universal quantifier (a semantic object). The quantifier symbol "∀" binds to a variable symbol such as "x," and the (semantic) universal quantifier binds to a (semantic) variable such as x. Although the "∀" symbol can be described in purely syntactic terms (by appealing to substitution), at a semantic level, it must be understood in terms of semantic interpretations. Specifically, it states that the formula evaluates to true under every interpretation of x (possibly subject to other requirements, such as the axioms of the surrounding theory).
