You can pronounce it but its common to drop the n when something ends in "en". That means that natives are likely to say "lopuh" and "etuh" instead "lopen" and "eten".
That is true. But after goeden is the next word avond. So then al Dutch people say de 'n'. The same as an apple. Nobody says a apple I think. The woman who says goede-avond without 'n' has not the good pronounce. Sorry my Dutch is better than my English. I hope you understand what I mean to say.
How to properly pronounce 'v' in Dutch? Here, on duolingo it sounds more like german 'v', but from what I found on other sites it's really more like english 'v'. And a guy form Belgium I know was quite surpised when I told him that german 'v' is really 'f'. :) So, what's correct way to say it in Dutch?
I think it depends on the region of the Netherlands you're in. My relatives from the Hague tend to pronounce it like an English "V". So there are different accents I think.
How come goedenavond has an N in the middle, but goedemorgen doesn't? Is it a remnant of an old case system?
Yup, it should be gendered case system where the -en ending is because 'avond' was a masc. noun and in the accusative case with its adjective agreeing. It was once the object of a now ignored verb.
What I'm taking from the given pronunciation is that the 'n' in 'goedenavond' (among other similar terms) isn't emphasized, correct? So, if I were to spell it out it would have the 'n' but when I say it the 'n' is pretty much non-existent?