What you don't understand is that Black Moon is not an object like asteroid Lilith or even Dark Moon Lilith(which may be a dark matter planet). And so you can't square a point in space, you can only square an actual object.
BML is only a point in space, so you can only have a definition of the interaction in a conjunction. Fixed stars are essentially the same. Since they don't exist inside the solar system, they are essentially points and you can conjunct them, but you can't have other aspects to them.
As to your chart, its pretty easy to deal with, in that there are no serious restrictions in it. But the downside is that you also don't have the experience of a difficult Saturn or Mars etc. And your low latitude Moon suggests that you don't tend to take the bull by the horns, and when you do react is is emotionally. This means that you are more likely to be blown around by the winds of events in your life. But that strong Uranus makes it hard to focus as you tend to want your freedom to act. So you have an open-ended birth chart with few serious restrictions, but not lot of experience or focus in dealing with the difficult moments in your life---thus your interest in Lilith squares.