In the audio, the final i's are pronounced as separate words in both filii and mei, which is wrong.
Yes, you are quite right. There are no glottal stops (a glottal stop being that gap in the middle of "uh-oh") in Latin, except, I would guess, in the traditional German pronunciation.
I doubt myself a little with this one. Is 'mei' genitive and 'filii' nominative in this sentence?