Only one specific character missing when compiling with biber and xelatex

Using fontenc with XeLaTeX is wrong, because the engine uses Unicode which is based on Latin-1 for the lowest block and T1 doesn't coincide with Latin-1.

The glyph ğ is covered by T1, but it is in a position that can't correspond to the glyph as XeTeX sees it, because it is not in Latin-1. Other glyphs have the same problem; others that are in Latin-1 are in different positions in T1.

Either use pdflatex or load fontspec instead of fontenc. Note that inputenc will do nothing, but it's better to remove it, too.

\documentclass{article}
\usepackage{fontspec}

\usepackage[<options>]{biblatex}

\addbibresource{mylibrary.bib}

is the correct preamble (add the rest). Note that \addbibresource is recommended over \bibliography (the .bib extension is required with the recommended command).

Do not use fontenc with xetex, you are specifying T1 encoded fonts which is a non-unicode encoding with just 256 characters, biber and xetex want unicode so you get in the log

 Missing character: There is no ğ in font ecrm1200!

ğ is U+011f so can not be in a T1 encoded font that only has slots up to FF

Instead use

\usepackage{fontspec}

and delete

\usepackage[T1]{fontenc} % Unicode in references
\usepackage[utf8]{inputenc} % Unicode in references