Covering of women hair

Re: Covering of women hair

i am reading that up all, but as i said earlier the pieces don’t fit together. some scholars say that indeed the hair covering is not specified in the Quran but it is proven by the hadith of Muhammad SAW, the other group of scholars that say that face and hand covering is also mandatory rejects the hadith as weak where Muhammad SAW said that women can show face and hands. So, if the ruling can not be established on a weak hadith, and the hair covering is not specified in the Quranic ayats, then how is it established that it is mandatory to cover hair.
Also, the word Khimar means a cover, not necessarily a head cover.
even if you say that it is pointed towards the head cover and the verse means that women should cover their bosoms with their head cover, then does that mean that today women who are using a head scarf to cover hair and are wearing a loose fitted thick shirts to cover their bosoms without using the the head scarf to cover it, are not doing the hijaab as it is required??