French nasal sounds and other stuff

I feel so inadequate, because I cannot tell the difference between on (allons), an (roman), en (inventer), and in (americain), in French.

To my American native English-speaking ears, they all sound very, very, similar. Do you have any advice for learning the differences in sounds?

Also, regarding the French in Action recordings, when Professor Capretz says "Nous allons inventer une histoire," why doesn't the "ns" in allons elide (is that the right word?) into the inventer?


And, lastly (I have a lot of questions today, sorry!), I really like the music of French-language singers and songwriters like Camille, Carla Bruni, Celine Dion, etc. In other words, poppy or pop-rockish kind of music. What are some similar bands or groups I should check out?

Grand merci!!