Given grammar, a nonterminal, and a string, does there exist a parse tree that uses the nonterminal?
You are asking two different questions, I will answer only the first one.


  Is this language T-recognizable? 


Designing first recognizer and then transforming it into a decider will not always work. A language may be undecidable but recursively enumerable.

Your approach is correct. This language is recognizable (recursively enumerable). Just systematically generate all possible sentences (for example by breadth first search algorithm) every time by checking if any derivation contains the nonterminal $A$ and the derived sentence is $x$. If the test passes then ACCEPT.

A hint for the second question: $x$ has some certain length $n$. Can derivation of all sentences of length $n$ help us decide?

Also, a decidable language is also recursively enumerable, but the converse is not always true.