Your teacher should probably have told you that if you want to get a sound out from 니은, "ㄴ", you should probably read the character "느" out loud. As far as 네 sounding like "떼", that is just one of the other variant of saying 네. That is an exception. The pronunciation of ㄴ is always the ㄴ in 느.

Its pronounced "n" in 안영하세요. Its only pronounced like d when it is in the beginning of a word :)

isnt it 'ne' ??