Was Elizabeth Bennett Gullible?

I have been re-reading Pride & Prejudice and have come to the conclusion that Elizabeth Bennett is gullible.

Alright, hear me out because this is interesting.

In the beginning of the novel, we know that Elizabeth makes a judgment on Mr. Darcy based on his words to Mr. Bingly within her hearing...no, that isn't where I begin to believe she is, because in the statements made by Mr. Darcy himself, which were rude.

But it is the whole deal with Mr. Wickham where we see her truest failings.  

Alright, so the man was charming and he was handsome according to everyone he came in contact with..I understand that, but my questions have been raised by this:

Elizabeth had barely been introduced to Mr. Wickham the day before when he starts questioning how well she knew Mr. Darcy and how he was received in the neighborhood...I would have raised an eyebrow at this to begin with, why would a total stranger start asking me personal questions about another man?  Then he proceeds to tell her of the "dastardly" dead and ill treatment he had received at Mr. Darcy's hands...again, I would start to get extremely suspicious of this and ask him point bland why he was telling ME, a virtual stranger to him, this tale and why only to me?

Elizabeth is a 21 year old young woman.  She has been described as a very intelligent girl with whit...why does she so readily believe this man when she doesn't even know him?  
Now, she tells her sister Jane about this tale of woe done to Mr. Wickham, she says that Wickham had facts to verify his story, yet here again is my finding on this...there weren't many facts or dates involved in the incident to be believable...and he refused to tell everyone else in the room because he claimed he couldn't dishonor Mr. Darcy's father...where were the dates and facts except his claim that he had is living taken from him by Darcy?

Even her sister Jane, who is a kind hearted person cautions her against believing the whole of it until she hears more on the subject, or better yet, let Mr. Darcy defend himself against the man.

It makes me ask another question:  Why didn't Elizabeth think when Mr. Wickham didn't show up for the Netherfield ball that there may have been more than one motive for his avoidance of the ball entirely?  Like, how about this...being called out for the liar we find out he is by Mr. Darcy himself? 

There was also something else interesting.  Elizabeth believed Wickham so much and accepted his tale, that when she danced with Mr. Darcy, she had a perfect opportunity to ask Mr. Darcy himself about it and let him defend himself as he could.  She didn't, instead she provoked an argument with the man.

It is also interesting to me that Elizabeth would believe the worst in the Bingly sisters and not be surprised by their bad behavior towards Jane but not look at the elephant right in front of her and question him.  She was also willing to believe the worst in Mr. Darcy based on First Impressions.

Here is another reason for why I believe that Elizabeth is gullible...when Mr. Darcy finally defends himself against the accusations laid at his feet in a LETTER, she readily believes him and accepts what he says as the absolute truth.  Then again, here is where our dear Eliza starts thinking about the oddities of the earlier conversations with Wickham and finds she had been blinded by prejudice and the original offense he gave by hitting her in her pride with his first statements.

I find it interesting that Elizabeth would believe Wickham because of what he had said, but it takes Mr. Darcy writing to her to change her mind and opinions.

Of course, Darcy could have said anything he wanted to about Wickham and Elizabeth would believe what he had said, she was quick to start changing her opinions of Darcy and Wickham after this.

I know this is what makes the story so great and shows the change in human minds and hearts when we realize we were wrong when we first meet people, and in a century where men and women had to follow rules set forth by society, it seems odd that impressions were made without getting to talk and know each other as they could have had they lived in our time.  

I just wonder why Elizabeth was so easily fooled by one man and then was quick to believe the other man in the end.