I definitely prefer selectors like main article header h1 over #main-content .post-body .post-header h1, just for readability's sake if nothing else, but I'm not super worried about specificity issues personally. It probably is preferable to keep your specificity low when possible.
main article header h1
#main-content .post-body .post-header h1
I think the HTML element you typed got filtered out; can you ask your second question again with backticks around the element?
<div class=container> The element is a white rectangle centered in the middle of the page.
So, the semantic elements introduced in HTML5 are all about conveying the structure of the data. Purely stylistic elements, like containers that only exist to help make the CSS work the way you want, don't have any semantics to represent, so a plain
old <div> really is the correct choice there, no replacement necessary.
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