Did you find the solution to your problem? I'm having a similar problem. I'm unable to view the fonts I've used in my epub file (created in InDesign CC) when I view it on the Kindle Direct Publishing previewer when I go to publish it. Any advice would be appreciated.
To find your fonts you have in your epubs(embedded), try crack opening it up in sigil or other such epub editor, there you can find the list of fonts in the epub. Also, if you want to see the fonts you have used in the InDesign document there is an option saying find fonts in the type menu of InDesign.
Also, to your query regarding the supported fonts!!, I agree this is quiet tedious job figuring it out yourself and may be any information may not be sufficient considering the huge amount of fonts we have.
But still apple used to release some font list that will be supported. I didn't know the actuals for which you are seeking, for e.g. iOS7 you can find it here.
You can similarly find for others too.
Probably a starting point could be the fonts listed on the actual device:
- Original ( I guess this relates to an embedded font)
- Helvetica Light
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