In US English, word final T is almost never released, other than in the citation form, or when people choose to make a recording of their pronunciation for the whole world to listen to, which is why Forvo is the worst place to hear natural pronunciation. Of course, the true native speaker is usually not consciously aware of these phonological processes, and will deny reality. Based on your recording, I’d say you are better qualified to answer your own question than most native English speakers, so the best thing to do would be to listen to real conversation, where native speakers do not know you’re paying attention to their pronunciation. In the meantime, here are some specific guidelines for the final T in American English: 1. Usual option: Unreleased (and unaspirated) T. 2. If the T is preceded by a vowel (sound) or R: Use the so-called quick-D (actually an alveolar flap). Example, both Ts in “That it is.” “Part it on the right.” 3. Same as #2 but T is preceded by N. The T will usually be dropped, but the preceding vowel will still be shortened as if the T were pronounced. “Do you want a….” “Can he or can’t he?” 4. Before a Y sound. There are several options, one is the “blend,” which sounds like a CH. “Don’t you?” This option is very popular in UK accents, including RP. 5. Before an N, and possibly some other sonants (including Y, if option #4 is not used), the T is often realized as a glottal stop. “What really matters is….” Note: A lot of Australian and UK speakers use the glottal stop as their usual realization of syllable-final T, not just before a sonant, but even between vowels in the middle of a word. 6 If #5 applies and the T is preceded by F or S, then the T is usually not pronounced, although native speakers will claim they’re pronouncing it. “Last week.” The T may also be dropped between two Ss “scientists” 7 When speaking very quickly, the T may assimilate to the next consonant in terms of place of articulation. “Let go” /lekgo/

As with many features of American English, daily conversation and professional settings may have different rules governing when to pronounce and when to not release the T. Because conversation happens so quickly, the T at the end of words is almost always left unreleased and almost never heard (unless a person speaks with an accent and/or dialect that does so). So to answer your question, yes, it's perfectly okay to hold the T at the end of words without pronouncing it. I believe the only instances when the T isn't held or pronounced at all are French loan words that have retained their French pronunciation (e.g. "ballet").

I really don't think there's a set "rule". I just checked forvo.com for "faucet", and about half of the speakers (all American) didn't release the "t". So it really is half-half. My advice is to listen more, decide if you like what you hear, and if you do, then copy it. :)

I'm not 100% sure but I believe any word that has an ending with -et sounds like this. I found this website helpful as well with pronunciation. https://forvo.com