Open, also known as The Open Video Hosting Project, is an entirely handwritten website template, designed for those wanting to make their own YouTube alternative or (using API keys) clone. The name Open is sort of a pun on it being open-source. Currently, it is only in Alpha, meaning some features aren't complete yet, but you may feel free to contribute to the Open Project if you want to, see TODO.MD for what needs to be done.
More detailed information about hosting your own Open based site can be found in HOSTING.md, but to simplify it, all you need is a server computer, a website hosting platform (like Apache2), any SQL Database, and some PHP and SQL knowledge and your set for life with your little Open site. By default, Open uses MySQL for its default SQL database, if you're going to use another SQL database service, you might need to change some of the PHP files.
Yes, but you'll obviously need to change the files.
Not really, there are some more common rules you and your userbase must follow described in RULES.md, but you can pretty much make your own rules regarding mature or adult content in your Open site.
You can contribute to Open as long as you have a basic understanding of the PHP language. See TODO.md to what needs to be done.
The early web-esque look of Open was intentionally done since Open's UI/UX is based/inspired by early YouTube. You can give your fork a more modern feel if you want.