Allright, I want to be forthcoming and straightforward with you. As far as the missing emails. Since you never accessed your mail through an email client, such as mac mail, thunderbird, outlook 2011 / 2016/ etc..
There isnt a hard copy backup of your email that we can restore. You went to the only place that could help you with those missing inbox emails, optimum.. And hopefully they will help you restore them.
All that I can do for you is either
A. I can help you setup your mail account with an email client, so in the future you have a hard copy of your emails in case your online mail server gets cleared out. Also, I could help you check your phone and mac and make sure you didnt pick up any spyware or malware when you were on public wifi that may have allowed someone to access your mail account.
Or B. I can send you the refund link now if you dont want to do step A, as considering the specifics of your situation as we discussed it, I cannot help you recover the mail. There simply isnt any way to do so other then through optimum.