The employer may state anything it deems appropriate to the EDD, as it provides its side of the reason for your separation. Based on the information provided by you and the employer, the EDD will make an initial determination whether you are eligible for benefits. If you are denied, you have the right to ask for an administrative hearing, which must be submitted to the appeals board within 20 days from the written notice. At the hearing, each side may present testimony and evidence to support their respective positions. Based on the evidence, an administrative law judge will decide whether you voluntarily quit, without good cause or were fired for misconduct, either of which would be the legal basis for denial of benefits.
It is completely up to you to decide whether you wish to use this former employer as a reference. Just know that employers are only obligated to be truthful. If it believes the truth is you were fired for cause or it has a negative opinion of you, it has the right to say so. Some employees choose to use personal references, such as a manager you may have had a good relationship with, for contact, rather than the company itself.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
They can make the argument. It will be up to you to show that you quit with "good cause," which in turn will require you to demonstrate that a reasonable person genuine desirous of remaining employed would have been compelled to submit their resignation under similar circumstances. Even then, it sounds like there is an issue with misconduct if there is any truth to your employer's allegations that you attempted to "turn" other employees against them, so there's no guarantee of success on appeal.
You cannot prohibit potential employers from contacting your former employer. The only way to prevent that from happening is to omit your former employer from your resume entirely. This, of course, poses other problems.
This answer is a general interpretation of the law and is not fact specific to your case. Likewise it does not create an attorney-client relationship. You should seek an attorney for a review of your specific facts and documents.
You cannot prevent the EDD from communicating with your former employer. The EDD must communicate with the employer.
As to your right to benefits, you have two issues you have to work through to win your appeal. First, your leaving of the job cannot be a "voluntary quit" as that term is applied by the EDD. Second, you cannot have been terminated for "misconduct" as that term is applied.
Please take a look at the following links that comprehensively discuss both concepts. Study these links to determine if you can avoid an adverse finding under both approaches. If so, be prepared to prove your case.
Good luck to you.
This answer should not be construed to create any attorney-client relationship. Such a relationship can be formed only through the mutual execution of an attorney-client agreement. The answer given is based on the extremely limited facts provided and the proper course of action might change significantly with the introduction of other facts. All who read this answer should not rely on the answer to govern their conduct. Please seek the advice of competent counsel after disclosing all facts to that attorney. This answer is intended for California residents only. The answering party is only licensed to practice in the State of California.