Does a married woman need to cover her hair when making any brochas for herself? if so what is the source?
No, there is no specific obligation for a woman to cover her hair when reciting blessings.
Although some are stringent in this matter, it appears that at least for Ashkenazim, one can be lenient.
Concerning covering hair for blessings, see Shulchan Aruch, Orach Chaim 75:2, and Mishnah Berurah 14. This refers only to men who are able to see a woman’s hair as they recite the blessing, but not to the woman herself.
Based on the rulings of the Shulchan Aruch (96; 206:3) whereby a person must not recite a berachah with his head uncovered, some — and in particular Sefardic authorities — rule that even women must cover their hair upon making a berachah. Rav Ovadyah Yosef thus rules that even according to the modern custom whereby unmarried girls generally don’t cover their hair, they should do so when making a berachah.
However, I have not seen Ashkenazi poskim who are stringent in this matter, and the universal custom is that girls recite berachos with their hair uncovered. There is no apparent reason to distinguish between married and unmarried women in this matter, and therefore for women who do not cover their hair at home, it is permitted even to recite berachos without covering hair.