Encontrei o livro que procurava?
Nope, this structure is called "Future Perfect" in English and yours is Simple Past.
" terei encontrado o livro que procuro?" parece PT-PT
I would even say "terei eu encontrado o livro que procuro" in PT-PT. What is the most natural BR-PT form?
In previous examples in this section I believe that they have been using the form "procurar". Is that possible for here also?
You can use the verb procurar but you need to conjugate it.