Thank you, Sitesurf, for your nice explanation. If you don't mind, could you please explain something else as well? Is there any connection between the rule about the position of "dernier" etc, and the usage of male/female forms of nouns like jour/journée and and an/année ?
Is it always l'an dernier ... as a date, and la dernière année .... as a subject/object ? Because I think I've seen both: l'an dernier and l'année dernière .... as a date I guess. And in your example: " il parle du dernier jour qu'il a passé ici " I would think I was supposed to use " journée " .... but apparently you can use " jour " here.
The rules pertaining to the use of jour/journée, soir/soirée, matin/matinée, an/année are a pain in the neck for learners.
Basically, "an" is used when you count years and "année" when you refer to the duration of a year.
However, this rule is kind of polluted by some fixed phrases that do not all comply with the rules.
Maybe take a look at this page which summarizes the rules: http://french.about.com/od/vocabulary/a/an-annee-jour-journee-matin-matinee-soir-soiree.htm
thanks, another question: I've seen a lot on comments section that the end of such these words is written as: der-ni-yey, or for example "avez" pronunciation has been written az a-vay somewhere in comments section, but in some online dictionaries I have heard them, for example "dernie", as "hear" without pronouncing the ending "r" of course, or for example "avez" as "avii", the i: like something we see "see" or "bee" so dernier or avez or... are pronounced something like ævey or ævi: pronunciations are sometimes hard to differentiate for even the same female voice this way or that way on Duolingo... may someone clarify that plz? and also do we have something like stress or emphasize on words syllables just as we see in English, in French too?
To answer your last question, there is no syllable stress in French, only sometimes word stress if you intend to emphasize some elements of your speech.
I gave you a link to IPA for French, because it is a reference for English speakers. I assume that other phonetic alphabets can be used by other language speakers.
I also gave you a link to Forvo where French natives speak out words so that you can accustom your ears to hearing 'real' French (vs Duolingo's TTS). You may use it as often as you have a doubt on the way a word sounds here. Google Translate also has good audio and some dictionaries also have speakers as well.