is it permissble for a woman to make a brocha or say kriat shema with out her hair covered?

It is permitted for married women to make a Brachah, say Kriat Shema or pray with their hair uncovered. Nevertheless, many women have the custom to cover their hair while praying or making a Brachah even in the privacy of their home. Regarding single girls, it is the custom of all Ashkenazi girls and most Sephardic girls not to cover their hair at all even while praying or making a Brachah. Some of the great Sephardic Halachic authorities maintain that single girls should cover their hair at least during praying Shmoneh Esreh and Bircat Hamazon, but the common custom even among the Sephardic girls is to be lenient and not to cover their hair at all. (הליכות בת ישראל פרק ה, סעיפים ג, ה, יא, ובהערות. יביע אומר חלק ו סימן טו. פניני הלכה תפילת נשים י, ו).