I want to make my own website with
Adding my videos
Chating
Pictures
Leting my friends putting posts on it
Music & (music videos)
Contests

I really want my friends to hung out on it everyday
Is there any website I make like that?

Sure. Where have you looked?

The same thing is called Facebook.

Sounds like a Yahoo group to me

Content management systems like Joomla and Drupa are both free to install and offer plugins to do everything you wanted to do. Face book will also work along with Blogger and Wordpress (Wordpress can be used for free at wordpress.com or you can install it on your hosting account) . Using a CMS like Joomla or Drupal will require that you buy a hosting plan, but they will also give you your own domain.Hosting can be had for between $4 and $10 a month for shared hosting (mutable sites ran from one server works well for small to medium sized sites with low to medium traffic) depending on the length of your contract.
Joomla and Drupal are easy to use if you have good computing skills with an understanding of web hosting and there are a lot of places to get free help.

I use webs.com it works perfectly for your description and is easy to use...