Purely from my observation (so I might be wrong) the "n" seems to be added where there might otherwise be a "stop" in the flow of the sentence. It seems a bit like when English uses "an" instead of "a".
As for the non-pronunciation of the "t" I think that's something you just have to get used to.
Judging by my Vietnamese wife and her friends, pronouncing the ends of words strongly isn't very important in Vietnamese, not nearly as important as getting the tone correct. It is interesting because it carries over into their English, for example my wife says "fi" instead of "five" and "smi" instead of "smile".
When I tell her to finish the words she says that she did. And then we fight about it because she clearly didn't.