Kindles do not have support for ePub. You need to convert them to a Kindle format.
If using calibre, I would recommend converting to AZW3 or KFX (the latter requires KFX Output plugin and installation of Kindle Previewer 3) rather than MOBI. AZW3 is functionally the same as MOBI but about half the file size.
You can also convert ePub to KFX with
send-to-kindle service.
If you got an error sending via email, it could be the email address you sent it from is not white-listed, or the ePub has some formatting errors in it.
In any case I would use the Web send to kindle as it lets you supply Title and Author metadata, and accepts larger ePub files. You can also monitor progress there.