"Can I safely asume that links between subsites on a subdirectories based multisite will be treated as internal links within a single site by Google?"

At best.

Unless they're otherwise straight-up  professional links with zero spam intention, I wouldn't use them.

Don't  worry about all that  header stuff; Google doesn't (very much).

Are your most important words in the topmost locations in your html? That's what you want to care about. Are you  using them in your initial headings? Are you using them in your initial  sentences and paragraphs?

But remember, it's not just about "keywords" it's about supporting/complimentary vocabulary. If you're just throwing your keyword into copy that is otherwise fluff ( contains little topical concepts and terms), you're not going to beat out other sites that do.

Nick,

It's kind of a head smacker when you think of it.  It makes sense that the order of the words in the query would make a difference in ranking. Different orders may mean different things. Also, since google is trying to match the searcher's words to potential websites that satisfy the searcher's intent, the order of words on a website definitely a site's ranking for specific keywords.  Those these may be only subtle differences between  site's copy, but still, someone has to rank at the top for a particular order and someone still has to rank at the bottom for that same order.   It's the algorithm.

Calvin,

If the content on the page  with the backlink is relevant to the content on the page it is linking to, that's good. If the anchor text on that link is also relevant, that's even better.

If content on the page that the backlink is pointing to is not of a relevant or complimentary subject, google will weigh the value of that  link less.

If you change the URL of a page that is being linked to from another site and do not properly redirect the old URL to the new URL, the link will not benefit the new URL at  all.