Some words like "jeg", "er", "den" (which is sometimes replaced by "han", or shorter, "an") come in very many forms, depending on the dialect. And as you say, it's almost inaudible. After all, "min" is the important word in this sentence, and gets the most focus
I can definitely hear a "dn" there (without the e), but I'm German and we tend to do that a lot as well
This happen when d/t/n/l/s letters come after the "r" letter. (you just ignore the next letter (d/t/n/l/s) after the "r". This isn't just an ignore action, but I do not know the technical language name of it)
"miN" is for masculine nouns "mi" is for feminine nouns But in this phrase, we dont know if the subject (det) is feminine or masculine, so I dont know why they used "min". Is it optional? Could I use "mi" instead of "min" on this case? Ex: Det et mi?