Regarding a man being able to see a sister without her hijab, this is actually true.
I myself was unaware of this until I took Al Maghrib's Fiqh of Love course by Sheikh Waleed Basyouni and saw that this is in the details of Islamic Fiqh regarding marriage.
How much of a woman is a man allowed to see in order to make his decision? Is her permission required?
"The vast majority of the 'ulema are of the opinion that the sister's permission is not required and in fact it is better not to take her permission. The wisdom behind this recommendation is that it could be very embarassing for a sister when a brother visits with the intention of getting married; however, doesn't find her attractive and therefore rejects her solely based on her physical appearance.
Vast majority of scholars including Imam Shafi'ee, Imam Abu Hanifah, Imam Malik, and Ibn Hajar hold the opinion that one is only allowed to see her face and hands, nothing else! They claim there is no need to see anything beyond this and seeing hands and face should be sufficient to decide if one wants to marry this sister or not. Her face would indicate her beauty and her hands should give you an idea of her body size. From a fiqh perspective, one is not allowed to look at women in general as men are commanded to lower their gaze. The only reason they would look at a woman is out of necessity for engagement, but it should be kept to a minimum.
Imam Ahmad and Imam Awzaa'ee disagree because a woman's real beauty shows without hijab. They state that she is allowed to show whatever she shows at home - her face, neck, arms, and feet. Scholars who hold this opinion claim that Prophet Muhammad SAW didn't specify to Jabir to only look at her face and hands. He told him to "look at her" and according to the Hadeeth Jabir saw her while she was in her tent - the chances of a woman being without her hijab is much higher in this circumstance. He may have actually seen her inside the tent and something that he saw helped him make up his mind to seek her hand, despite being previously married and having children (it might have been her appearance or even her behavior)."
Wallahu Alim.