Is that "Mostly Water" as in "Ugly bags of mostly water" by any chance? (a Star Trek joke, for those who are wondering - this is how humanoids are described by a race of crystalline life forms).
To answer your question about tonguing notes, the answers for jazz and for classical are diametrically opposed. Simply stated, the distinction is this:
In jazz, unless otherwise indicated, notes are to be phrased together (i.e., not individually tongued) unless you're deliberately playing staccato as suggested by the rhythm, or there are markings of some kind, like staccato (.) or tenuto (_) above the individul notes. Tonguing is almost a special effect.
In classical, unless otherwise indicated by phrasing slurs or indications like "legato," notes are to be played as discrete entities - tongued, in the case of wind instruments. As you rightly note, this is obviously not practical in the case of trills and very fast passage work
In terms of the basic performance practices of jazz and classical music (by the way, both of these contain numerous historical and regional substyles with sharply contrasting performance practices), tonguing has no relation to whether you are changing breath or hole as you move from one note to the next, but there is an important phrasing benefit to be realized through tonguing in some instances (I detailed this in the chromatic workshop in HIP No. 3).
By tonguing the FIRST note of a two-note group that involves a breath change (i.e. you're playing blow G followed by draw A, and you tongue the G) you can create a GREATER disruption in the tonguing that makes the breath change sound smooth by comparison. You can tongue normally- nothing exaggerated. I know this sounds crazy but it works. I got it from Robert Bonfiglio by way of Paul Farmer, an Australian player.
On the chromatic, legato (smooth progression from one note to the next with no discernible break in continuity) is disrupted every time you change the direction of your breath. Which the tuning pattern forces you to do a lot. So legato is like gold, and certainly I wouldn't make a practice of stopping the breath every time you move the slide. One cool thing about slide changes is that they DON'T break up the legato. If you move the slide too slowly, you'll get two notes at once, a semitone apart (this was used very effectively once in a western soundtrack), but as long as you move it normally, there's no reason to stop the breath.
If you're listening and thinking with this kind of attention, I don't think you're in much danger of developing "sloppy" or "weak" technique, as you seem to fear. Listen to how the music sounds when the experts play it, then listen to the sound you make. Generally, at a good music library, or even with a couple of good books, you can read up on the performance practices of the style you want to learn, and this will help clarify practices.
