At the risk of stating the obvious, playing the flute requires us to breathe quite frequently. You could try to hide this breathing entirely by learning a technique such as circular breathing, but it ends up being counter productive in this musical genre. In other genres it can sound great, but here it tends to make the tunes sound monotonous and we miss out on the opportunity to use our breath points as an ornament. So, we take breaths that are audible, in the sense that they break up the continuous flow of sound coming from the flute.
The first thing to realize is that this can be turned to our advantage in making the music sound more interesting and in enhancing the rhythm. A breath is actually one of, if not the, most powerful rhythmic ornaments. This means that if you insert it at the right point in the tune it will greatly enhance the rhythm, but at the wrong point it can sound really inappropriate. Breaths taken at the optimum points are often almost unnoticeable because they reinforce the rhythm so well. Where the optimum points are located varies from one type of tune to another, primarily because the rhythmic structure differs. For example, the notes you might choose to miss in a jig are different to those you might choose to miss in a reel.
So, there are legitimate and illegitimate potential breath points that are imposed on you by the rhythmic structure of the tune you are playing, i.e., the tune type constrains your choices. But there are still very many possibilities in terms of where you could legitimately take a breath in any given tune. Usually, many more than you actually need.
If you take breaths at very regular intervals, the phrasing that results will sound a lot more repetitive than if you vary the location and length of time between breathing points. Variation in breathing pattern, and phrasing that results from it, can be used to add a bit of interest when you repeat parts of a tune, again to make the repetition sound more interesting. Or in some cases you can deliberately play certain parts of the tune with the same repetitive pattern in order to emphasize them. If you play with regular breath intervals/phrasing and then insert a longer phrase, that longer phrase will be more prominent than if you always varied. There is a lot of scope for imprinting your own personal style or interpretation on a tune this way.
So, a lot of what I just said is pretty straightforward, as a foundation. You can practice trying to play a tune as many different ways as possible, while still following the basic rhythmic rules about which notes to drop. But what you’ll probably find is that some seemingly legitimate places for taking a breath just don’t sound good. This is because there is more to good phrasing than simply rhythm. There is the question of how it interacts with the melodic structure of the tune. Certain sequences of notes are important and shouldn’t be broken. Certain sequences can be broken, but only in certain ways, and that might require a note substitution or switch in order to sound “right”. So there are issues of taste which kind of merge into questions of legitimacy in terms of what is traditional, or traditional for a particular region, etc. This is where listening and trying to soak in the kind of language or accent of the music is important. Some players are particularly creative when coming up with new and interesting phrasing. There are people on this forum who have been immersed in this music for a very long time and who can speak to these later issues much better than I can. Its a rich and interesting area.
So back to some of your specific questions.
On the relationship between phrasing and breaths: you should generally take a breath before you need to. Well before, usually. Taking the breath introduces a phrase boundary. Just make sure its at a good place and try not to be too repetitive about it.
Phrasing it not tied exclusively to the call-response pattern, but the call-response pattern in a tune can certainly influence your phrasing.
When you learn phrase-by-phrase, you can think of it as just learning each phrase as a mini, stand-alone, tune. It makes it much easier to get your finger programmed for the sequence of movements. Then you can start trying to string them together, maybe initially in pairs of phrases, etc.
I hope this helps. I’m sure others here have a lot more to add.