Does a husband need the wife permission to get a second wife? If the permission is not needed then if the wife is not happy about won’t that be an act of zhulm against the wife not being fair which goes against the quran.
If you also know any booklet i can read this subject in details.

Also why do sunni on hajj expose one of their shoulder while shia cover completely?

Also if you know a book i can read on the ritual of hajj and how to perform them and also why these things are done and their history would be helpful

Yes permission is not condition but according to Quran justice is condition which not easy as Quran described
Holy Quran 4:129
وَلَن تَسْتَطِيعُوا أَن تَعْدِلُوا بَيْنَ النِّسَاءِ وَلَوْ حَرَصْتُمْ ۖ فَلَا تَمِيلُوا كُلَّ الْمَيْلِ فَتَذَرُوهَا كَالْمُعَلَّقَةِ ۚ وَإِن تُصْلِحُوا وَتَتَّقُوا فَإِنَّ اللَّهَ كَانَ غَفُورًا رَّحِيمًا

And you will never be able to be equal [in feeling] between wives, even if you should strive [to do so]. So do not incline completely [toward one] and leave another hanging. And if you amend [your affairs] and fear Allah – then indeed, Allah is ever Forgiving and Merciful.
Our some of the Sunni brothers they expose one of their shoulder they are following their school of thoughts. Reason only they can provide