If you have more than 180 days of unlawful presence, you need a waiver as you will be subject to a three or 10 year bar. If you do not need a waiver, your eligibility will be determined based on your submissions and the discretion of the consular officer.
Depending on the language of the reinstatement denial letter, you may not have unlawful presence.
But, you could have difficulty convincing the US Consul to give you a visa.
Does the DSO support you? If so, a letter from him/her will be of great value ... as will consulting with an attorney.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
It doesn't seem you broke the 180 day unlawful presence invoking a 3 year bar on admissibility. With that said, overstaying is a serious violation leading to a denial. You can bolster your case by getting a letter from the previous DSO explaining their mistake or the reasonableness of the miscommunication. You should consult an immigration attorney to help guide you through the process.
Possible. You don’t have a bar though. But it’s still discretionary.
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You can get a visa provided you convince the consulate and that depends upon your explanation for overstay. Your reinstatement application and denial would be considered too. If the old DSO could explain some of it, it would do you good.
My answers are for general information only, NOT A legal advice because these are not tailored to your specific situation. Contact an Immigration Attorney if you need legal advice.