phineas and zac efron (i forgot the name of his character) take over 5 shots of liquor each in a bar/singing scene. they are never seen getting drunk though.
I would say no however, there is a scene where Barnum is kissed by Jenny lind without his consent however there is not mention of it being an assault or any flashbacks to it
A character is burned, while they are alive ; but if the question means Is someone burned to death" then No. They are rescued within about 30 seconds, and another character states they are still alive. They are then shown in a hospital bed, but no injuries are visible.
There is an intersex woman with a beard who is enlisted as one of P.T. Barnum's "freaks" to be laughed at. It's portrayed as uplifting, rather than degrading.
This whole movie misrepresents the disabled community's history. P. T. Barnum was a real person that was highly abusive to disabled and biodiverse folk, along with other minorities such as POC and queer folk to name a few. (He did a number of awful atrocities that I won't go into here, but I encourage you look into it if you want to know more.) This movie created a false narrative of him being a benevolent person to make an inspirational story out of the sufferings of many.
The movie is very loosely based off of a real person (P. T. Barnum), who was incredibly ableist, and his harmful acts still impact the disabled community to this day. This movie takes his exploitation of disabled people and turned it into an "inspirational" fictional story.