The reason Dorian Gray decided to murder Basil was a sudden feeling of hatred towards Basil. As the novel states, "Dorian Gray glanced at the picture, and suddenly an uncontrollable feeling of hatred for Basil Hallward came over him, as though it had been suggested to him by the image on the canvas, whispered into his ear by those grinning lips."
As for the effect, there was none on Dorian. He was able to sleep though the night without worrying about what he had just done. "The man had to touch him twice on the shoulder before he woke, and as he opened his eyes a faint smile passed across his lips, as though he had been lost in some delightful dream."

The interchange between Dorian and Alan was quite intimate, however filled with hatred. The novel lets us know that Dorian and Alan were, at one point, best of friends. However, there seems to be an event where Alan no longer wished to be a friend of Dorian's, and so they went their separate ways. When Alan first arrived at Dorian's house, Alan stated "I had intended never to enter your house again, Gray. But you said it was a matter of life and death." After going back and forth talking about their deteriorated friendship, it gets to the point where Dorian is forced to blackmail Alan in order to get him to dispose of Basil's body. From there, Alan never wants to see Dorian again.

The reason Alan made a visit to Dorian's house was because Dorian had sent a messenger to Alan's estate with a message stating that Dorian needed his help in a "life or death matter." This matter just so happened to be the murder of Basil and it could have ruined Dorian if the public found out about it.
The effect of Alan's visit is that he is forced to help Dorian as he blackmailed Alan. Dorian had written a letter and addressed it to a certain someone; when Alan read the letter, "his face became ghastly pale and he fell back in his chair. A horrible sense of sickness came over him. He felt as if his heart was beating itself to death in some empty hollow."

The symbolism can be seen in the "red dew that gleamed, wet and glistening, on one of the hands [in the painting], as though the canvas had sweated blood." This is symbolic of the murder of Basil.

I can only guess that the letter is written to a current lover or institution that proclaim's Alan's abusive homosexuality. The reason I say this is because of this line: "You treated me as no man has ever dared to treat me--no living man, at any rate. I bore it all. Now it is for me to dictate terms."

There are two ways that the dinner party can be significant in relation to Dorian living a double life. The first is the fact that the party was being held by Lady Narborough and many other females would be there that, according to Lord Henry, Dorian could flirt with. However, we clearly know that Dorian has an affinity for men. This is a prime example of his double life.
Another example of his double life is when we find out about Dorian's addiction to opium. He treasured going into a stingy, run down Opium Den and meeting with "Adrian Singleton," a low-life opium junkie. Yet, he attends this high class dinner party a day earlier? Clearly a double life.

What is particularly ironic about her statement is that Lord Henry isn't anywhere near as wicked as Dorian has, and yet she is stating that Dorian is a "good man" as he looks and was made to be good.

The statement means that in order to cure your soul, sometimes to need to take a step back and enjoy things the world offers. Yet to cure your physical being, you first need to cure your soul. As we discover, Dorian indulges in a lot of drugs, sex and violence. This is what he strives for to "cure his soul" and therefore his senses. Specifically in chapter 16, Dorian seeks an Opium Den in a rough part of London to cure his soul by means of the sense, and his sense by means of his soul.

There are two things revealed about Dorian. The first, and most obvious, is that he is addicted to Opium and this particular Opium Den is his regular stop for a fix. We can tell this from when he first walks in and heads directly to the location where Opium is smoked, calls out a name who responds "Where else would I be" and has a fit with a women whom he obviously does not like. The second thing revealed about Dorian is that he should be in his forties, but because he looks like he is twenty, he is able to fool James Vane.

The Opium Den is located in a "dark lane" near the waters edge where "Over the low roofs and jagged chimney-stacks of the houses rose the black masts of ships." The Opium Den is "a small shabby house that is wedged in between two gaunt factories." Inside hangs a "tattered green curtain" and there are "flaring gas-jets, dulled and distorted in the fly-blown mirrors that faced them, that are ranged round the walls." Further into the den is a staircase that leads into "a darkened chamber."

When the woman calls out "Prince Charming," the sailor sprawled out on the table immediately gets up and chases after Dorian. Why is this? It is because the sailor is James Vane and remembered before her sister passed away that she used to call the man that indirectly killed her "Prince Charming." Now he seeks to avenge her death.
Although Prince Charming may have meant a handsome gentleman, it also means "A man who ardently seeks the company and affection of women." So although the woman was calling Dorian Prince Charming, it was for both definitions.