In Pride and Prejudice by Jane Austen, who says the following sentences and to whom?'I hope we can still be friends now we are brother and...

This kind of question asks you to consider what you know about the characters. Even though there are a lot of characters in Pride and Prejudice, by looking at any snippet of dialogue, you can often tell who said it and to whom the sentence was spoken just by thinking about what the dialogue means and its tone. In other words, this is an exercise in thinking about characterization. 

But if you can't figure out who said these quotes, you can always just search your electronic copy of the novel to find them quickly. Unfortunately, this strategy only works if the reported bits of dialogue are accurate. This particular list seems to consist of bits of dialogue that have been paraphrased, or misreported, or perhaps taken from one of the movie adaptations of the novel. They don't appear in the novel itself.

Let's consider each one:

1. "I hope we can still be friends now we are brother and sister?"

No one says this in the novel, but Elizabeth says something similar to Mr. Wickham near the end of Chapter 52:

"Come, Mr. Wickham, we are brother and sister, you know. Do not let us quarrel about the past. In future, I hope we shall be always of one mind."

What she means is, "Now that you're my brother-in-law, let's not argue. Let's be friends."

2. "Please come to dinner on Tuesday, and you can bring your friend."

This sentence does not appear in the novel, nor does anything similar to it. However, in Chapter 3, the Bennet family is intent on inviting Mr. Bingley to dinner, and they also meet his friend, Mr. Darcy. Mrs. Bennet is eager to marry off two of her daughters to these handsome, rich men, so she wants to establish a social relationship with them. A dinner invitation is never expressed to them in this way, however.

3. "You will not believe how rude that girl was! I am so glad you are not thinking of marrying her!"

These sentences also don't appear in the novel. In fact, the only time people talk about rudeness directly is when they say some particular social misstep is "abominably rude."

However, this sounds like something that Mr. Bingley's sisters would say to Mr. Darcy about Elizabeth. They are snobby and disapprove of Elizabeth's outspokenness.

4. "I always liked him! Even when other people said he was proud."

These sentences also don't appear in the novel, but here's something similar that Elizabeth's aunt says about Mr. Darcy to Elizabeth in Chapter 43:

"There is something a little stately in him, to be sure," replied her aunt, "but it is confined to his air, and is not unbecoming. I can now say with the housekeeper, that though some people may call him proud, I have seen nothing of it."

Of course, you can always argue that Elizabeth would say something like this herself, in reference to Mr. Darcy, perhaps to her parents or to her sisters. She had a hard time convincing her family that she not only likes Mr. Darcy, but loves him. This is because earlier in the novel Elizabeth, like everyone else, thought Mr. Darcy was haughty.