How aware is she about her shape-shifting?
She could regularly wear a concealed suit underneath her normal clothes, one that would accommodate her size or form as she changes.
About the Irregulars' rarity, it could be a genetic combination of very specific genes and DNA.
Due to the vast and countless DNA combinations possible, the Irregular gene would be a tiny percentage.
I'm glad I could help with the name, and I hope my other ideas can help you as well! Happy Thanksgiving!!
Just to clarify your question #1, you want powers that are genetic but not heredity(passed down from parent; right? I have several ideas:
A) Epigenetic changes are made after fertilization, often after birth. They are caused by environment, including the mothers hormones, and affect how genes are expressed or even if they are expressed. Google "epigenetics" for more information.
B) This idea is more far-out: A great deal of our DNA does not directly produce proteins which affect cell function; decades ago this majority of our DNA was erroneously called 'Junk DNA.' At least a portion of this DNA is composed of non-functional mutated genes from past ancestors (including the remains of viral DNA) the the cell has wrapped up but not done away with. Instead, with every cell division, this chunk of unusable DNA is copied and stored by the daughter cells; just like I have a few books from my grandparents on my bookshelves that I have no intention of reading, and will probably pass them on to my children. Idea is that your protagonist takes a compound that reactivates one or more of these inactive genes; could be genes from a virus or from a werecat ancestor.