To understand Babadook's powers/abilities, one must know, first of all, what exactly is the Babadook? Is it an evil spirit, a mythological monster, an actual creature or just a symbol?
Babadook is the impersonation of Grief & Problems.
The wikipedia entry itself answers a lot of questions
Writing for the Daily Beast, Tim Teeman contends that grief is the
"real monster" in The Babadook, and that the film is "about the
aftermath of death; how its remnants destroy long after the dead body
has been buried or burned". Teeman writes that he was "gripped" by the
"metaphorical imperative" of Kent's film, with the Babadook monster
representing "the shape of grief: all-enveloping, shape-shifting,
Amelia is a single mother grieving over her husband's death and finding it very difficult to cope with the responsibilities of parenting.
The director Jeniffer Kent has stated that
she sought to tell a story about facing up to the darkness with
ourselves, the "fear of going mad" and an exploration of parenting
from a "real perspective". In regard to parenting, Kent further
explained in October 2014: "Now, I’m not saying we all want to go and
kill our kids, but a lot of women struggle. And it is a very taboo
subject, to say that motherhood is anything but a perfect experience
With this background, let's go back to your original question:
What are the powers of the Babadook?
This question can be rephrased as
What are the negative-effects of not being able to cope up with your grief and your problems?
Babadook can do what grief and problems can do to someone, someone who is not coping well. And this very thing is very subjective and varies from person to person, situation to situation.
And how is the monster defeated?
By acknowledging it. Acknowledging one's problems and standing up to them.
I think at the end, Amelia acknowledges and accepts the fact the her husband has indeed gone forever and she must overcome the hardships of being a single mother. This eventually weakens the monster within her and she feels empowered again.
From the same source:
Teeman states that the film's ending "underscored the thrum of grief
and loss at the movie’s heart", and concludes that it informs the
audience that grief has its place and the best that humans can do is
As for Sam's magic tricks, I see it this way:
What happens to kids who have troubled parents at home? They are troubled themselves, not able to do good themselves.
And what happens when their parents become strong?
They too become strong and able to unleash their unlimited potential.
Hence the great magic tricks.