I long ago lost track of the various retcons and reboots that have altered the DC multiverse in the past several years. In particular the entire New 52 came and went before I could become more than passingly acquainted with it. So I beg your indulgence in explaining stuff to me. Beginning with Captain Marvel:
What was the deal with Mary Marvel’s various uniform changes (red-black-white)?
How did Black Adam change from a villain to an anti-hero (or at least, a villain the heroes needed on their side against worse villains)?
I think the white was to just make her more visually distinct from Billy. (She’s back to red, now.) The black was…an unfortunate storyline. She was possessed by Desaad, and thus evilized. Which is not an entirely bad premise inherently, but it was part of Countdown to Infinite Crisis, which was poorly planned and worse executed. But it did give us the hilarious image of Mary using Kyle Rayner as a bludgeon.
The original personality of Teth-Adam reasserted itself, and the more villainous Theo Adam was purged. Teth-Adam was still a bit on the brutal side, but he became a member of the JSA, until he set out to liberate Khandaq.
Captain Marvel was the most successful and popular comic book of the 1940s. It was published by Fawcett Publications. Around 1950 or so, DC decided to sue them for copyright infringement, saying the Big Red Cheese was based on Superman. As the trial wended its way through the courts, the market for comics shrunk (partly because of Frederick Wertham and Seduction of the Innocent). Fawcett decided to get out of the business, so the settled the suit and stopped running Captain Marvel.
The trademark was not being used, so in the 60s, Marvel created their own Captain Marvel and trademarked the name.
After that, DC bought the rights from Fawcett. But because “Captain Marvel” was trademarked, they called the comic book Shazam. The character was still called “Captain Marvel.”
Eventually, DC decided to stop using the name, since Marvel had their trademark and guarded it relentlessly. So they renamed the character to match the title of the book.
Only indirectly. The books (and TV series) had been Shazam! for as long as DC has been publishing them, because of Marvel’s Captain Marvel… In 2009, they gave up on fighting the I Am Not Shazam battle and just gave the character the name.
DC first sued Fawcett for copyright infringement in 1941. The case dragged on until 1953, when, as you noted, Fawcett withdrew from the superhero market and settled the infringement case with DC.
What nobody ever mentions is that the guy behind the DC lawsuit was Dr. Thaddeus Sivana. He’s no dummy, HE knows the best way to defeat that Big Red Cheese!