Was Wudang Sect being set up during Song dynasty or end of Yuan to early of Ming dynasty? There are alot of stories as to when it was being set up by Zhang Sanfeng...

Also, various martial arts sects like Hengshan Sect, Huashan Sect, TieJian Meng, Beggars Sect and Songshan Sect, were there realy such sects in history?

earliest documentary of 'Wudang' appeared in the Hanshu. It has been a sacred site for Daoism since the Tang dynasty. But it wasn't until around the Ming era that it was it was recognised as a martial arts school. As for Zhang Sanfeng, those stories are just what they are, stories. There are no reason to believe the guy even knows martial arts outside the folklores and novels. Historical documentions are inconclusive if whether he was even around. And most stories of him intenting Taijiquan has been blasted to pieces already.

Most of the other 'sects' you mentioned are either pure fiction or have little to do with martial arts. They are merely religious sites where temples are built in which practicing of Qigong is more about health and spiritual cultivation rather than having any martial arts intentions.

The begger sect has been explained here
http://www.chinahistoryforum.com/index.php?showtopic=13522

Serious, because I was reading a book on the origins of chinese martial arts and it talked about huashan sect, so I thought huashan sect actually existed in history. So Ermei sect is also fake?

I believe it might be in your favor to get an idea of the school system of martial arts so you can understnad what a 'sect' means

Relevent information can be found here.
http://www.chinahistoryforum.com/index.php?showtopic=11013

I get the general idea of sects and systems, but what I have from the book "origin of chinese martial arts", it said that Huashan Sect did exist... that's all... I am just trying to find out more that's all.