Is there a sense of justice in Bronte's Jane Eyre? If so, in which parts of the novel is there justice or injustice?

In Brontë's Gothic romance, Jane Eyre, justice is a theme that runs throughout the story.
Jane Eyre, an orphan, lives with her aunt, Mrs. Reed; she is taunted by her cousins, deceitfully blamed by her cousin John for his misbehavior, and treated harshly by her aunt—who unfairly accuses her of having the worst sort of character flaws.
It is not without irony that the reader recognizes justice for Jane—even though her character seeks none. The Gateshead coachman tells Jane of John's fate:

"Why, you see, Miss Eyre...[John's] life has been very wild: these last three years he gave himself up to strange ways, and his death was shocking [...] he ruined his health and his estate...he got into debt and into jail: his mother helped him out twice, but as soon as he was free he returned to his old companions and habits. [...] How he died, God knows!—they say he killed himself."

Eventually, Mrs. Reed comes to express her regret for her behavior toward Jane, on her deathbed.

Well, I have twice done you a wrong which I regret now. One was in breaking the promise which I gave my husband to bring you up as my own child; the other— 

Mrs. Reed has kept a letter from Jane's uncle, hidden from her niece:

I took my revenge: for you to be adopted by your uncle, and placed in a state of ease and comfort, was what I could not endure. I wrote to him; I said I was sorry for his disappointment, but Jane Eyre was dead...

Mrs. Reed's punishment is not in death, but in her realization that all she had done against Jane was wrong. Facing imminent death, she recognizes how much she hated Jane and how much she resented her late husband's care of the child, as well as Mrs. Reed's broken promise. Despite Mrs. Reed's hatred of her niece—alone in the world—Jane not only survived her years at Lowood and made something of herself, but she also now had an uncle who very much wanted to have Jane in his life.
As a young child, Jane is taken from Gateshead, rejected by Mrs. Reed and her children, to the Lowood Institution, a school for poor girls. There, Jane recalls how badly she was treated at the Reed household. Helen, Jane's best friend, points this out to her.

...but how minutely you remember all she has done and said to you! What a singularly deep impression her injustice seems to have made on your heart! 

Helen acknowledges the injustice, but tries to convince Jane to let these feelings go.
At Lowood, the children struggle terribly. They are punished harshly for the smallest infractions. They walk two miles to church during the winter, almost "paralyzed" by the cold, from which they have too little protection. Jane struggles because she is always so hungry: the older girls, also famished, bully food from the younger children. The school's patron, Mr. Brocklehurst, is formidable and cruel. Early in their association, Jane hears him explain his ideologies with regard to raising these young girls, telling Miss Temple:

You are aware that my plan in bringing up these girls is, not to accustom them to habits of luxury and indulgence, but to render them hardy, patient, self-denying.

There is no kindness or philanthropy in Brocklehurst.
Brocklehurst is a clergyman, but his character is anything but Christian. It is only when typhus fever arrives at the school and so many die that the conditions under which the children have lived are finally exposed. For the next eight years, things greatly improve. Mr. Brocklehurst is relegated to treasurer, in which he has no control over, or access to, the girls. There is justice in this as Brocklehurst is removed from his position of oversight—where this man who insisted he was a Christian authority is now unable to do the girls harm. There is justice, too, in Jane's success at becoming not only a good student, but also a young woman of good character. The religious Brocklehurst has insisted that he knew what behaviors a young woman must exhibit to avoid the fiery pits of hell—and that Jane was a failure in this area. Justice is apparent in that Jane proves that Brocklehurst was wrong about her, as she grows to be the model of a godly woman, in direct contrast to Brocklehurst's hateful and misplaced accusations.
Edward tries to marry Jane while his first wife still lives (locked away in madness at the top of Thornfield). Perhaps justly, Edward loses the love of his life when Jane leaves, for she is unable to live in the same house while still loving him. Ultimately, Edward's wife, Bertha, escapes from her room and burns down Thornfield. Ostensibly as a result of Edward's lies, justice of a terrible magnitude is visited upon him. Not only has he lost his home, but also his sight and a hand in the fire. 
There is also, however, a merciful side to this justice. Edward knows why Jane had to leave and has suffered through it. He stayed at Thornfield where Bertha was, rather than running away—leaving England, as Jane had feared. He even attempted to save Bertha when she ran out on the battlements after creating the inferno surrounding her. In this, Edward receives symbolic redemption: a broken man, Edward is rewarded with a second chance—in that Jane loves him despite his broken state. Because he is willing to swallow his ever-present pride, Edward and Jane's love is requited. They had chosen to do the decent thing and live apart: he, in the face of his marriage vow, and both of them by being faithful in their love for one another.
Examples of justice are found throughout Jane Eyre.