The -e ending is not just for plurals, it is for all definitive nouns too. So it makes sense, here is a summary:
en stor bil (a large car). no suffix.
et stort dyr (a large animal). -t suffix
store fester (large parties). -e suffix
And then for all of the definitive cases, it is the -e suffix.
den store bil (the large car).
det store dyr (the large animal).
de store fester (the large parties).
Hope that makes sense.
A "definite noun" is a certain object, where in English you say "the house". (Or my, your, that, this house.) The indefinite case is "a house" in most cases.
In Danish that starts making a difference when you use adjectives which will then take on their definite (-e) form:
- et stort hus - a big house (indef)
- det store hus - the big house (def)
- mit store hus - my big house (def)
- and so on
In most cases, definite and plural adjective forms are the same, so you have:
- store huse - big houses
- de store huse - the big houses
- mine store huse - my big houses
- and so on
Going through the Hungarian course (where they use an actual recorded voice), I've seen that many people have problems distinguishing the voiceless plosives k, p, and t if they're in weird places. Those sounds are probably not all that different from each other.
It does sound like a 'k' to me here, but that might just be me hearing what I want to hear. The pronounciation is okay here. In this sentence I would pronounce kok like the English "cog" (since the following sound is a voiced one, [l]) and in isolation I would swallow the second 'k' pretty much.
Danish pronounciation is pretty complex, and there are a couple of words that are spelt the same but pronounced differently, like "I read" and "I have read" in English. (I wonder if the English courses on here have that problem as well.) The TTS does the pronounciation of the sentence automatically, but sometimes trips over these.
The DDO gives the pronounciation of lave as [ˈlæːvə], so the fast version is closer to the official pronounciation. It might also have dialectical reasons.