As someone who is a huge fan of her character and acting in Game of Thrones I am super excited for what her expanded role will be in the next movies. I agree that she wasn't given much to work with in this movie but I do have the following points to add to your questions.

A) I 100% disagree that Phasma was cast as Gwendoline Christie just for "progressive" reasons or to fill a quota. She was amazing as Brienne of Tarth on Game of Thrones and I can't imagine the studio pushing for her inclusion if the writers objected. If that were the case she would not be the only woman on Starkiller Base. I think that her being a woman in such a position of authority has a lot of story subtext because, as you mentioned, the Empire was not exactly pro-gender-equality. For her to be in command tells you that she is a badass without having to show you she's a badass. That will hopefully occur in the next movies, once she crawls out of the ~Sarlaac pit~ trash compactor.

B) Although they didn't include any mention of this in the movie (and I'm not sure how anyone could have without it being clunky) her armor actually has a pretty badass backstory. In the Visual Dictionary that was released with the film, the armor was actually made from parts of one of Palpatines personal space yachts after his death and the decline of the Empire. The reason it is shiny is because it is made from Chromium (the same stuff all the silvery ships from Naboo were coated in) which means that that suit of armor is not only superior protection against blasters (made from the hull of a starship) but is also insanely expensive, like (Republic senators stopped using it for their personal luxury ships because it was so expensive). Her flashing that as part of a uniform approved by the high command of the First Order would be like Frodo strolling into Minas Tirith with his Mithril Armor on full display.

C) You are correct about the origin of the name being from the Phantasm movies, but she got it because a main obstacle throughout the series is the floating silver sphere that punctures people's skulls before drilling out their brains. JJ was apparently tickled by her armor's resemblance since it's shiny and silver as well. Here is a picture of the death sphere for comparison: http://i.imgur.com/Y4TiYRl.gif

D) This ties back to point A in that, film-wise, we have never seen a female in any position of power. This means that there has to have been some first-class offscreen ass-kicking on her part because the Empire doesn't seem to put women in a lot of power positions.

I have my own theories about her possible role in the upcoming movies and I'm sure that the writers have something awesome planned. I definitely don't think she's a Fett as it seems the writers actually have something planned for her in future movies as opposed to being dropped in the mouth of a sand mollusc.