This one's really fun to overlap the recording.
"ses, sseeps, osskeeps, nossaŭkeeps, dnosseaŭkeekps, dnoseaŭkekp, dnoeaŭkk, dnaŭek, dek"
"e" in Esperanto sounds more like the "e" sound in "egg". The "a" sound in "ape" is closer to the Esperanto dipthong "ej".
Yes and no. Esperanto vowels are "pure". That is, they are supposed to be one sound the whole way through. English vowels move around a lot. (Think about how much your mouth moves when you say the O in "go").
So, the difference in Esperanto between "e" and "ej" is that "e" is pure and "ej" moves around a bit.
What Sanguine_Dreamer seems to be asking about is vowel quality. It's possible to pronounce E in different ways that are pure (i.e. that don't move around a lot) yet which remind us of different English vowel sounds. I know fluent speakers from different countries who pronounce E in ways that might sound like "a in ape" to some people. There's nothing wrong with this, although it did surprise me at first. The voice in Duolingo pronounces it a bit like the E in get, and that's fine too.
Along these lines, watch out for a popular Esperanto speakers who pronounce "i" like the short "i" in English (lid, kid, kick). Shoot for a good "eeeeee" sound. I've heard a few German Esperantists pronounce it that way, but it's not ideal.
Esperanto Stack Exchange (Tomaso Alexander)
YouTube (Esperanto Variety Show)
Duolingo Esperanto Learners FB group.
Mi estas cxie. :-)
On a tangent, it kind of irritates me that «unu» breaks the nice one-syllable pattern of the other numbers.