I think part of the confusion is that these are not actually technically questions. They are "unknowns" being used in a statement:
エリートにも まだまだ解らない事が あるものです, 何故アナタがまだ 私を見捨てずにそこで 戦い続けているのかも, 何故 私がそこに向かおうと しているのかも
Even as an elite, there are still things I don't understand, both why you haven't given up and are still fighting for me, and why I'm heading there.
These "why"s are not actually questions of the listener to answer. They are simply statements of things the speaker does not know. The か particle can also be used for this purpose within a sentence, to mark a phrase as something "unknown" that is being referenced, for example:
なぜそうしたのかを考えています。
I'm thinking about why he did it.
The other thing to notice is there are actually two of these unknowns being stated:
何故アナタがまだ 私を見捨てずにそこで 戦い続けているのか -- "why you haven't given up and are still fighting for me"
何故 私がそこに向かおうと しているのか -- "why I'm heading there"
These two things are then being connected using the AもBも construction to say "both A and B".
So these のかもs are actually three different particles. の turns the verb phrase into a noun, か marks it as an unknown thing or "open question", and も..も is then being used to connect the two things together as a single subject/topic.
This last part of things is, of course, an incomplete sentence. To be a complete sentence, you could add something like「解らない事です」("..are things I don't understand") on the end, but the meaning is pretty obvious from context even without it, I think.
