1.) It's called the h1 element
h1 Element = <h1></h1>
h1 beginning tag = <h1>
h1 ending tag = </h1>
It is improper to refer to an element as a tag unless you need to specifically
reference the start or ending tags which is rare.
2.) There are two headers on your local newspaper for the day: your country just won a war and your grandmother's chair was stolen by a duck; which one do you think has the highest priority? Would you use that priority for every heading?
Remember the level of the heading directly correlates to the value of the page's content and you should never use a header to style the font-size, you should only use CSS to do styling.
In general I treat the h1 element the same as the title, it should be descriptive about what the page's content is about. Here is an example of how headers generally should look like with some fake filler content for the sake of example...
<h1>Acme Co's New Blue Widget for Webmasters!</h1>
<h3>Do Not Add Water!</h3>
<h3>Example exploded hair pictures from improper uses</h3>
Also keep the numerical order of your headers in check. If you're using h6 it means in the code it's below an h5 element (as a child) which is below an h4 element (as a child), etc etc.
Using (X)HTML elements in their proper context is a great way to master (X)HTML. I also recommend using XHTML 1.1 and serving it as application/xhtml+xml for learning and if you're really good for live use. What you can achieve is only limited by what you allow yourself to aspire to. ;)