Hi Hanah and others, please ignore iamluckystar. This person is just a troll who is hating on Love and Redemption specifically, and his/her explanation is also wrong.
Adding on to Hanah:
Xianxia is a Chinese genre which involves fantasy. In other words, we have immortals (gods/goddesses), demons, mortals, cultivation (practicing martial arts/magic), and obviously, the Three Realms. Demons are part of Xianxia, and anyone who has watched any Xianxia will be able to confirm it. (besides haters) The Three Realms consists of three different worlds: The Heavenly Realm, The Demon Realm, and The Mortal Realm. They are all connected, and the realms will not be able to exist if one realm disappears.
To Hanah: Tian Xu Hall is a group of cultivators who have turned evil. Some are demons, but not all of them are. When a person practices evil magic for too long, he or she will slowly become a demon, although that doesn't necessarily mean that all demons are evil.
Xuyang Peak is, yes, a branch of Shaoyang Sect. It is also the most important branch, as it is led by the sect leader.