So, am I allowed to add the symbol to my website ?

Such as Videos, Images, Advertisements etc…
~ Somewhere, out there.

Definitely Maybe. Trademarks do not protect websites directly. Trademarks protect consumers. Trademark law seeks to prevent consumers from becoming confused about who is selling, sponsoring, originating or is otherwise the source of a good or service. So, you would not be trademarking the website (unless you were building websites for others), you would be trademarking the services (or goods) that you provide at your website.

A trademark provides certain rights. For example, when a competitor marks its stuff (goods or services) in such a way that a customer might become confused (likelihood of confusion), the trademark holder can sue the competitor. Sometimes, there are other remedies, like UDRP proceedings to help with domain names and cybersquatters.

If you want to claim a trademark, you may need to first search to be sure that you have some right to use that trademark, that is, make sure that you do not infringe on the rights of a competitor.

Then, you may wish to apply for your own trademark, at the federal or state level. Or, you may wish to rely on your common law trademark rights. To make decisions about when to perform trademark clearance searches and what trademark applications to file, it is best to consult with an attorney.

For more information about how and when to use the trademark symbol, read this article:

How to use the ™ symbol

Good luck with your website.