you have got really nice name and your site looks like clone of temp-mail.org but thats fine. I have used temp-mail before and it was really good service, what you have to do next is add few more domain names to use as email address. In no time many services might ban use of @bitcoinemail.org emails so adding new low cost domains on each week will be good step ahead.
Still doesn't make his service ""Decentralized"", It is actually quite the opposite. His site is not even open source, let alone "decentralized".
The same argument could be said for your "decentralized" "Social Network Service" you bought domain / you pay hosting / you own servers so please spare me the debate on that. Its just yet another "word" anyone using bitcoin services anywhere should treat it as such.
"Is there any way we as a ""customer"" / User can check that? That would be very nice."
May be a way to do that by showing web access logs publicly. Have to consider that....
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How would you integrate something like sending emails in a blockchain? That sounds overly complicated, but i'm very curious to see how you'd do that.
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a upcoming open-source I will integrate as it is developed == hint one word "Volcano"