Firstly: 

We appreciate your keenness to find out the truth and follow it, and we ask Allaah to show us the truth as truth and enable us to follow it, and to show us falsehood as false and enable us to avoid it. The correct view regarding this matter is that it is obligatory for women to cover all of their bodies in front of men. See question no. 21134.

 Secondly: 

Your saying that “the rest of the Muslim women did not cover their faces” is not correct. Rather the command to observe full hijab applied to the wives of the Prophet (peace and blessings of Allaah be upon him) and his daughters and the believing women. The evidence for that is the verse in which Allaah says (interpretation of the meaning): 

“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e. screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allaah is Ever Oft-Forgiving, Most Merciful”

[al-Ahzaab 33:59]

 And Allaah says (interpretation of the meaning): 

“And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way, or outer palms of hands or one eye or dress like veil, gloves, headcover, apron), and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms)”

[al-Noor 24:31]

The command in these two verses is general and applies to all believing women. 

Al- Bukhaari narrated that ‘Aa’ishah said: “May Allaah have mercy on the first Muhaajir women. When Allaah revealed the words ‘and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms)’ they tore their aprons and covered their faces with them.” See also question no. 6991. 

Abu Dawood (4101) narrated that Umm Salamah said: “When the words ‘to draw their cloaks (veils) all over their bodies’ [al-Ahzaab 33:59] were revealed, the women of the Ansaar went out looking as if there were crows on their heads because of the covering.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

The Muhaajir and Ansaari women obeyed this command and covered their faces. 

Thirdly: 

With regard to a man looking at the woman to whom he wishes to propose marriage, this is part of the Sunnah. Abu Dawood (1783) narrated that Jaabir ibn ‘Abd-Allaah said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘When any one of you wants to propose marriage to a woman, if he can look at that which will motivate him to go ahead and marry her, then let him do so.’ I proposed marriage to a girl and I used to hide myself until I saw that which motivated me to go ahead and marry her, then I married her.” Classed as hasan by al-Albaani in Saheeh Abi Dawood, no. 1832. In the report narrated by Ibn Maajah it says that he hid in her garden to see her. 

This hadeeth indicates that the women of the Sahaabah used to cover their faces, because if it had been the custom for women to uncover their faces, there would have been no need to hide, because he would have been able to see her in any place if she had been uncovering her face. 

But because it was the custom for women to cover their faces, he needed to hide. It is well known that if there are no non-mahram men around, a woman does not cover her face, such as when she is in her house or in her garden, as in this hadeeth. 

And Allaah knows best.