What is the importance of the HTML DOCTYPE?

I recently asked a question here and the solution was a simple:
Now, my pages work fine in every browser without the doctype (except IE). Does IE need a doctype (is this an IE only thing) and do other browsers just assume it OR or is it doing something I'm not seeing.

HTML html, doctype 0 Answer

What is the difference between HTML and HTML5 ?

I've been making research about the tools that a front end developer shall know. Now, I'm focused on HTML and I have some questions that are listed below:

Since HTML5 is better than HTML and offers new tags such as header, nav, article, etc. why not everybody is not using them?

Why there are still old tags? Or Should I prefer to use HTML5 tags or keep using HTML tags?

Does HTML5 is supported for all of the browsers?

Do you have any comments, answers to those questions?

Thanks in advance..

HTML html, html5 0 Answer