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: Assuming that the film didn't underperform, would there have been a sequel?
Answer: A sequel is still possible, but PIXAR and Disney say there are no current plans for one. They are open to the possibility but claim to be moving away from a sequel-heavy slate to instead focus on original projects. Although it received good reviews, Onward under-performed at the box office, though that was partially due to the COVID pandemic. A sequel is doubtful, or, if there is one, it could be a straight-to-video DVD.
Question: At the beginning, Dolittle was scared because a boy broke in his territory, so he says to Chee-Chee, "Possum, play dead." Why does he call the gorilla possum? Chee-Chee is a gorilla, not a possum. Also Possum is not his name nor nickname.
Answer: 'Playing possum' is slang for pretending to be dead, as possums sometimes do that to avoid predators.
Answer: Opossums will go into a state where they appear dead when threatened, thus the term "playing possum." Dolittle was just saying to act like a opossum and play dead.
Answer: Ray was probably being sarcastic, and was simply making a general comment about gentrification in the area.