I love both
Beatrice and
Beatrix. They're both beautiful and strong names. I find
Beatrice a tad softer than
Beatrix, which has more edge, but I really do like them both equally.
The only possible nicknames (for both
Beatrice and
Beatrix) I can think of are
Bee,
Trish,
Trix, and
Trixie.
Out of your combos, I like
Beatrice Helen the best (though I personally find them all rather plain. I would rather see Beatrice/Beatrix paired with a slightly more unusual or at least edgier name. These combos are too "comfy" for my taste).