You can exclude certain terms with the - operator, as described in the Help Center. In this case, since the keywords you want to exclude, you have to make them exact matches with ". Searching for
"falcon" -falcon-9 -"falcon-heavy"
gives 133 results; it looks like it returns both posts using the word 'Falcon' on its own, and also 'falcon-1'. (I say looks ...
You can abandon the largely useless stack exchange search capability and use duckduckgo, which supports the negation operator much better than google.
falcon -spacex -heavy -9 -9s site:space.stackexchange.com works pretty well.
NIX doesn't really exist any more. It was one of the many redundant image sites NASA had, specifically one hosted at Langley. It used to look like this.
(internet archive link)
Note that the weblink today doesn't go anywhere.
I haven't tested them all, but results found through checking the NIX option on ntrs generally result in broken links.
My guess is that for some reason it things you are trying to use a non-english language, using something about how your OS and/or browser is configured. Still, this is strange... It did not happen to me, but it did happen to at least two users that really doesn't make sense. I'm going to tag it as a bug.
Hyphens are excluded from tag autocomplete. ion-thruster appears as you type ion-t or iont -- hyphens are ignored both ways.
Also, tag autocomplete is a full text substring match, not a prefix search, by design.
According to NASA itself,
The NASA Image eXchange (NIX) is a web-based search engine for simultaneously searching one or more of NASA's online image and photo collections.
As the saying goes, a picture is worth a thousand words, so they might be helpful (if you can't find an appropriate picture in any other way). But YMMV ...