After her father dies, Emily wants to have total control over her environment. She asserts this control by insisting on stasis: she wants nothing around her to change once she has her life organized the way she wants it.

Emily won't pay taxes after her father's death because her father was promised he would never have to. The town felt protective towards its aristocrats, because these families represented to it their collective nostalgia for a lost way of life. Therefore, the mayor concocted a story that the town owed the Griersons money, and for that reason they were exempt from property taxes.

Emily can no more pay the taxes than her father could—the town's people, in fact, knows she is poor, and look forward to her having to scrimp and save as they do. She is, however, arrogant and rigidly locked into place in her attitudes and ideas. Because her father didn't pay, she sees no reason why she should have to, so she doesn't. The town capitulates to her will.

Her refusal to accept free mail delivery is another sign of her rigidity, arrogance, and refusal to change:

When the town got free postal delivery, Miss Emily alone refused to let them fasten the metal numbers above her door and attach a mailbox to it. She would not listen to them.

Emily kills Homer because she wants to keep him with him her. She realizes she is about to lose him, so she poisons him. This keeps her life the same and keeps her in control of him, even if the "him" she has control over has now become a corpse.

Emily's extreme stasis is a sign of mental illness and symbolizes the "illness" of the South in being unable to move beyond its past.

It seems true that Emily could not afford to pay her taxes. Also important to note is Emily's tenacious claim over the rights given to her in the past.

She does not want to give anything up that she once had. This includes the house, the tax status, and the fiance that she keeps, dead, in a bed upstairs. 

In the story, Emily has been raised as a 19th Century southern lady, who would never deign to take care of such matters as taxes or house numbers herself.  Her father or the Colonel had always handled these situations.  When her father died, he left Emily with nothing except her home.  The Colonel knew her predicament and protected her by allowing the taxes to go unpaid.  As the years go by and new blood comes to town, the new mayor feels that everyone should be held accountable.  The house numbers and other such foolishness would not be tolerated by Emily.  In addition, she nor the servant could allow workers or anyone else too near the house because of the smell and for fear of finding out what was in the top floor.

Homer stumbled on a lonely woman, who desired him more than he wanted her. Because Emily wavers on the brink of sanity, she can not or will not take rejection. She needs him and wants him; these feelings are not returned. Deception is at the heart of embarrassment. No one wants to made a fool.  Homer would never be allowed to leave her, so a  plan was contrived obviously including the black servant because a tiny woman could never have killed, dressed, and placed the body in the bed alone. The truth to Emily was that if she captures and murders him, he will be hers forever. 

http://www.enotes.com/rose-emily/

Ms. Emily didn't want to pay her taxes because she couldn't afford to.  She truly believed her father had an arrangement where he didn't owe taxes, however she had no money to pay the taxes either.  Ms. Emily didn't like change and didn't think it was necessary to get house numbers.  She didn't want to change the house from the way it was when her father was alive.

As for poor Homer, Ms. Emily killed him because he was going to leave her.  She made such a public fuss with their relationship.  She couldn't bare the thought of him leaving her after all he had promised and the way he had treated her.  When he came to the house for the last time, she killed him so that he could never leave her.