Yes, but it makes hard the translations, and sometimes to sharply understand the right meaning.
[ʊ] is (similar to) u in put and [ɛ] is e in let –sometimes transcribed [e] in English. (In English accents these sounds often differ noticeably from their definition.).
Pay attention, these sounds occur in Latin where they absolutely can't occur in English.
[ʊ] - near-close back rounded (short), [uː] - close back rounded (long). The other two are a bit more complicated to explain. There are two phonemes: /e/ and /e:/, which correspond to [ɛ] and [e:] respectively. [ɛ] - open-mid front unrounded (short), [e:] - close-mid front unrounded (long). [e] (short) is an allophone of /e/ but can be confused with [e:], which represents a different phoneme /e:/. In the spirit of teaching how it should be pronounced and being prescriptive for that reason, the word 'studet' should be pronounced ['stʊ.dɛt].
The audio is wrong, since the stressed vowels are both incorrect. As AaronD.2 also pointed out it's "Fēmina studet.".
You claim to use Classical pronunciation but that is consequently false as of right now.
I've noticed that the audio is very weird for multiple reasons. For now, I'll chalk it up to a combination the course being in beta and the romans not having sound recording devices for us to use. However, if they come out of beta and it's still like this, then that's definitely not good.
There are some cases where the dative is not used with Studere. Which cases?