Question: When Phoebe is on the phone with Ray, he mentions that the Ghostbusters fire house is now a Starbucks. In the post-credits scene, we see that Winston has purchased the fire house so the Ghostbusters can get back to business, but the fire house looks like it has been abandoned for several years and no other company ever took it over. Did I miss something here?
Answer: Perhaps nobody wanted to take over the place for a few reasons. Historical purpose, high cost... hauntings.?
Answer: It's been 40 years since the Ghostbusters disbanded, Ray mostly likely passed by the old place and saw a Starbucks there. It has since shut down.
But they left the ghost trap active? Not likely.
Question: Why did Diana destroy the mall's security cameras, and why did she want the little girl to stay quiet?
Answer: At this point in time, her gig as a superhero is not public knowledge, and she wants it to stay that way.
How would that accomplish anything considering there were many people in the mall who saw what happened?
As the other answer indicated, Diana/Wonder Woman wasn't yet known publicly as a super-hero. A video recording is different from eye-witness accounts of what people actually saw or believe they saw. Memories are faulty, they fade, and everyone sees and remembers things differently. Regarding the child, I interpreted it as Diana just motioning in a friendly way for the rather precocious girl to stay put, behave, and quietly wait for her mother.
In my opinion, it wouldn't, and it's just another example of the shoddy writing in this film.
Answer: This was long before the age of superheroes, when everything was normal and meta-humans were just theories in a lab. It was her appearances which stated it all. Remember the tagline, "The Dawn of Justice Begins with Her."
Question: How come there was no dedication to Alex Trebek in the credits?
Answer: The movie was completely finished over a year ago. It was the pandemic that delayed it. So it was the finished product that was released.
Question: Since one male from each family in her village is required to report for training to serve the emperor, how is it that no-one recognizes Mulan - especially when she gives in to her chi?
Answer: Although it isn't said (in either this film or the animated original), she reports to a different camp than anyone else in her village. Otherwise, the men would not only recognize her physically but they would know beforehand that Hua Zhou never had a son so the ruse would never work. How she knows nobody from her village will be at that particular camp is never explained in either film.
Question: A helmet that is built to withstand thousands of PSI can really be broken by a few slams with a fire extinguisher?
Answer: Ray was probably being sarcastic, and was simply making a general comment about gentrification in the area.