H1 tags are usually reserved for the title of the page, or important stand out headings. It is possible for this heading to be halfway down the page but very unusual. The h tags do not necessarily need to be in order. They are used to organize headings by their importance. For instance you could have an h2 heading and have an h3 and an h4 heading in the same copy block and then start a new topic paragraph with another h2 heading and once again use the h3 and h4 headings within the next block of copy.
So no they do not need to go in order but their contents, relevance or organization is dictated by the heading used.