Mr Banks isn't abusive but is a strict and old fashioned father with little time for his children - some of his lines/behaviour could be triggering. He changes in the end.
An anthropomorphic umbrella (belonging to a woman) is asked to dance by an anthropomorphic cane (belonging to a man). The umbrella refuses, but is forced to dance anyway with it anyway. (In the sequel, 25 years later, the umbrella is still traumatized by this.)
Not necessarily? There are old-timey cops featured, the cop brings the children home when they get lost in the park and advocates for them against their father
Mary Poppins takes the children on multiple outings which feature impossible magical occurrences, including immersion into a completely cartoon environment. When they return home, reality returns to normal.
There is a reference to s*icide as characters worry about someone who has gone missing, possibly to a place "associated with jumpers". The missing character is found unharmed.
As the previous comment says, a cannon is fired regularly, but it is pretty obvious when the cannon will be fired, at several points Winifred calls the household to their posts and counts down, at others the Admiral himself counts down
No, but a man uses the racist slur 'H*ttentots' (a slur for African Khoekhoe) on a couple of occasions and uses it to describe imagined enemies, which carries imperialist connotations.