No, the dictionary and your H&J settings work in tandem — neither really “overrides” the other.
That is, if a word can be hyphenated according to the dictionary as “dic~tion~ary”, and your H&J settings (wasn't that a Quark term?) are set to at least 4 characters after first/4 characters before last, InDesign will fetch the possible hyphenation points from the dictionary, then discard the ones that don't work with the settings (and in this case none will be left, so it won't hyphenate this particular word).
The same goes for the Hyphen Limit; if ID already hyphenated the last word in three lines in a row, it won't hyphenate another one ever; regardless of what the dictionary says.
The entire system works like this: InDesign examines every possible combination of justification and hyphenation for an entire paragraph. That leads to a long list of possible breaking points; but all of them should be “valid”, that is, none of them will have less than four characters when hyphenated, and none of them will result in more than 3 hyphenated words at line ends. Then it assigns a score to each of these solutions, based upon (I think) how much the spacing would diverge from your preferred values per single line. A second run on the paragraph then tries to avoid a tight-set line followed by a loose-set one; that also gets lots of “negative points”. Finally, the mathematically best set of breaking points is used.
But the very first thing to do is assigning the correct language to all of your text! In your case it's not just the main reason for the badly broken words, it's the only reason. InDesign is extremely good in hyphenating “normal” text, and even does a fair job on specialized terminology (one of the reasons ID has a “medical” dictionary is because lots of medical terms are not based on English, but rather on Latin and Greek, which uses a different hyphenation system). Actually, most of the 'hyphenation errors' I encounter are in names, both foreign (“Sc-heidegger”) and, uhm, USA English (“Ma-cIntyre” — UK English hyphenates it correct!).
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