Do I have grammar mistakes? <3?

You do have several problems with both grammar and punctuation - far too many to correct here.

Be very careful about using the Information from the other two answers so far. Both start off by calling your initial sentence a run-on. That is just plain wrong, and anyone who says it is a run-on should not be trusted to give good advice on grammar. By definition, any run-on sentence must have at least two independent clauses incorrectly joined, and your sentence has only one independent clause - Bingley, his sisters, and Darcy depart for London.

run on sentence (try to split it into two sentences because it doesn't make much sense) :Soon after, Bingley, his sisters, and Darcy depart for London, announcing to Jane that they have no intentions of returning to Netherfield anytime soon and that Bingley will likely marry another woman, Miss Darcy, Mr. Darcy’s sister.

He tells her falsehoods about his relationship with Mr. Darcy, <<<and>>>that he was cheated out of a piece of inheritance from Darcy’s father.

This sentence doesn't flow well: Jane goes to stay in London after the Gardiners, her aunt and uncle, arrive and offer their residence for her upon hearing of her plight with Bingley.

say instead: Jane goes to stay in London with the Gardiners, her aunt and uncle, who offer her residence upon hearing of her plight with Bingley.

Elizabeth goes to visit Mr. Collins and her friend Charlotte, recently married and there <<<she>>>runs into Darcy again.

He however, gives her a letter explaining that Wickham had lied and that Jane had seemed largely disinterested by Bingley<<<,>>> so he warned against the match.

The two are married on the same day<<<,>>> and Mrs. Bennet is ecstatic.

This sentence: Bingley and Jane move to Derbyshire after a year and Elizabeth and Darcy live together in Pemberley with often visits from many of her friends.

Would make more sense if you said: After a year, Bingley and Jane move to Derbyshire and Elizabeth and Darcy live together in Pemberley, where they are often visited by their friends.

Good Luck

You have many run-on sentences. Check for clarity in your sentences and make sure your content is factual.

Example of run-on: Soon after, Bingley, his sisters, and Darcy depart for London, announcing to Jane that they have no intentions of returning to Netherfield anytime soon and that Bingley will likely marry another woman, Miss Darcy, Mr. Darcy’s sister.

Better: Soon after, Jane receives a letter from Miss Darcy and learns that the Bingleys and Mr. Darcy will depart to London for the winter. Jane's hope for a romantic relationship with Mr. Bingley is dashed when Caroline commented that Mr. Bingley seemed to favor Ms. Darcy (Chapter 24).

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Remember to check subject/verb agreement. Also, the events don't have to be direct order.

Example: Meanwhile, Elizabeth meets Mr. Wickham who she immediately is drawn towards.

He tells her falsehoods about his relationship with Mr. Darcy, that he was cheated out of a piece of inheritance from Darcy’s father.

However, Wickham soon takes up with another woman who he plans to marry and Elizabeth, after the careful warnings of her family leaves him be.

Better: Meanwhile, Elizabeth meets Mr. Wickham whom she is immediately attracted to. He deceives her about his relationship with Mr. Darcy; he tells her that he was cheated out of a piece of Senior Darcy's inheritance. Converse to his doting attention to Elizabeth, Wickham decides to marry another woman instead, and after her family carefully warns her, Elizatbeth gives up on him.

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Jane goes to stay in London after the Gardiners, her aunt and uncle, arrive and offer their residence for her upon hearing of her plight with Bingley.

She tries repeatedly to see him but is rebuked by Miss Bingley from even letting Bingley know she is in London and she slowly begins to accept the rejection.

Better: Elizabeth encourages Jane to stay with her aunt and uncle in London, the Gardiners. Elizabeth is sure that Mr. Bingley is in love with Jane and will come to visit her once he hears that she is in town. Jane accepts rejection after she attempts to see Mr. Bingley but is rebuked and deterred from Miss Bingley.

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remember to watch tenses...

A few days later Darcy returns himself and reproposes to Elizabeth to which she now accepts.

I think "reproposes" has to be "re-proposes" or just "proposes once again".

Tense-wise, "which she now accepts" should be "which she accepts." Remember that in "book-tense" the tense is always "happening". In one portion of the book, the character may have died, but in first half of the book the character is "alive". They are eternal, so the tense must be eternal. Elizabeth can always "accept" Darcy's proposal. It's a confusing tense so just go with it. :)

I'm sorry if I'm being too nit-picky, but I think that good editors are that way. I have many friends who trust me to edit their papers. If I had a copy of your piece, my edits would be in pencil. I think what the original author writes is important and editors are there to make helpful suggestions, but in no way should editors dictate style or content. Grammatical suggestions, however, are important to heed unless you're Hemmingway or Faulkner or ee cummings. Over all your piece is textually supported (although not supported textually aka, citations). thanks for being patient. I love the book Pride and Prejudice.