Yes, both D and T have exactly the same effect on the nasal sound in question because both are produced in exactly the same position; the only difference being that T is aspirated and D is not.
The pronunciation for official French from France remains as I stated above, however yes, you will hear a plethora of variations. Just imagine the word ‘good’ in English, the pronunciation varies enormously all over the world due to accent, stress, emphasis, tone etc. This is more or less the same phenomenon.
E vs. I (ɛ̃) / A (ɑ̃)
As in the table below you will notice there is no nasal E, but rather it falls into the nasal A or I category depending on the word.
- ɑ̃ - nasal a - an, am, en, em (sans, champs, vent etc.)
- ɛ̃ - nasal i - ain, aim, ein, eim, en, em, in, im, un, um, ym, ym (impair, daim, plein, pain)
- ɔ̃ - nasal o - on, om (un, parfum)
- œ̃ - nasal u - un, um (son, nom)
En and em are usually pronounced as the nasal A, BUT if they come after é, i or y then they are pronounced as a nasal I.
Prochain and Prochaine (and any other masc./fem. equivalents)
You are correct in hearing prochaine as more of an E. In the masculine version (prochain) everything moves back and up into the nasal cavity, whereas in the feminine version (prochaine), the end goal is dive forward to the front of the mouth and voice the N. From here on, I'm guessing a little and chalking it up to French euphony. This restricts the mouth and keeps it closed. To say an open A, you would have to first open you mouth and then close it to voice the N which is where the feminine stress should be.
For ‘official’ pronunciation refer to the audio in this LaRousse dictionary https://www.larousse.fr/dictionnaires/francais/prochain/64068
Accents (both English and French)
I hope I've answered your questions adequately. There is a tendency for me to struggle to explain pronunciation online like this due to the fact that many people have different accents and ascribe different sounds and pronunciations to different letters. For example, my New Zealand version of this E in ‘cement' might sound more like a blunt I.
Explanations are great (and I hope I'm helping), but they should always be used in tandem with other references, hence the link the the LaRousse dictionary above.
Another point to make here is to be wary of which French accents you are hearing. At Rocket French it should be official from France, but I've seen many resources out which inadvertently using Quebec French or another accent from a French territory for example. This is not hugely consequential but I thought it was worth a mention.
I hope this helps!