Covers
Usually, the first page of an epub contains the cover image. The epub format also defines a metadata entry that designates an image file in the epub as the cover.
EpubSplit, as I recall, does not attempt to designate an official cover image in the split epubs when 'Copy Cover' is off. I assume that is what is preventing Calibre from automatically using the first page as cover, but I could be wrong.
However, assuming that the cover is the first page of the epub (even if not designated as 'cover' in the metadata), you can use Calibre's 'Set book cover from e-book file' feature. In the individual book metadata editor, it's the button to the upper left of the ebook formats list. In the multiple book metadata editor, it's one of the options in the 'Change cover' group.
Once Calibre has cover images in the library, you can experiment with using Calibre's Polish or the Modify Epub plugin to push them back into the epub files, but depending on different factors, that may lead to duplicate 'cover' pages.
Calibre's 'Edit book' feature has the ability for you to explicitly designate which image is the 'cover', but it only works on individual books. The other tools can be used on several at once.
Fonts
I have forgotten basically anything I may have known 4 years ago about embedded fonts in epubs. The code is limited to "include all file with type 'application/x-font-truetype' in all output epubs".
It is entirely possible that your epub is different, but I would need to see it to know how.
If your source epub is not subject to copyright restrictions, you could post it here for me to see. Or somewhere else and send me a Private Message with the link.
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