I notice that final -i are almost silent in plural nouns. How is it for -i verbs though? the -i in ”a găsi” for example is clearly pronounced (according to the audio) but not so much in ”a auzi”.
It's actually not silent; it's just very difficult for non-native speakers to hear (or say) the difference. They are called "palatalized consonants". Russian and some other languages use them too. It may be helpful to search for this on Google, but mostly I think you need to practice with a native speaker.
the final "i"s in infinitives are sound (full vowels, stand alon syllables). The TTS bot is wrong here. "a a-u-zi", "a ci-ri-pi", etc. (see my discussion about ”un castravete doi castraveți”)