Compared to eating an ice cream cone, yes. Compared to calculus, no. Try these sites for listening to the sounds: http://french.about.com/od/pronunciation/a/beginningpronunciation.htm
Each definition may be for a different context. Some are for very specific contexts only. We don't expect every definition in a dictionary to work for every sentence. The main definition is "young" http://dictionnaire.reverso.net/francais-anglais/jeune It means new in a specific expression "jeune papa" and "jeune maman" mean "new dad" and "new mom".
If you hear a sound at the end of a word ending in -e, it is probably a schwa.
Interesting, thank you! The ending sounds does indeed sound like a schwa to me. However, isn't a key feature of French pronunciation that the "e" at the end of a word is left silent? It is my understading that having a "schwa" there is reserved for certain non-standard dialects and for artistic purposes.