What are the main differences between Luxembourgish and standard German from a morphological point of view? I mean, are there differences in the use of cases, noun-gender, articles, verb tenses? Thank you in advance.
There are three cases: nominative, accusative, and dative, but nominative and accusative have the same forms:
Definite articles: nominative/accusative-- de(n) [masculine], d' [feminine, neuter, and plural]. The "n" is added if the next letter is a vowel or n,d,t,z,h. dative-- dem [mas], der [fem], dem [neut], de(n). Same rule for adding "n".
Indefinite articles: nominative/accusative-- e(n) [mas], eng [fem], e(n) [neutre], eng or nothing [plural]. Same rule for adding "-n". dative-- engem [mas], enger [fem], engem [neutre], enger or nothing [plural].
Masculine adjectives always add "-e", Feminine add "-r" in the dative, Neuter add "-t" in nominative/accusitve and "n" in "dative", plurals always add "-n" when placed before the noun they modify.
The words of Germanic origin seem to have the same gender as German, those of Romance origin like French
Subject pronouns:
Ech (I), de (you familiar), hie(n)/e(n) (he), se (she), et (it), mir/mer (we), dir/der (you plural), Dir/Der (you polite), se (them)
Verbs: Present tense regular conjugation is to drop the "n" of infinitive, and add nothing for Ech, -s for De, -t for "hien/en, se, et" and "dir/der", "-n" or "-nn" for "mir/mer" and "se". Preterite has been replaced with present perfect and only a few verbs have a conjugation.
Future and present have merged. Conditional is formed with the auxiliary verb "ginn" and the infinitive which also means "give". The passive is formed with "ginn" and the past participle.
Some irregular verbs: soen (to say), wëssen (to know), daërfen (to be able to), doen (to do), verstoen (to understand), ginn (to give, to become, auxiliary be), hunn (to have), fuéren (to go).
In general this language seems to me more simplified than German, but complicated to learn for someone having studied German because everything is a little different. Even more difficult for someone who hasn't yet mastered German!
The use of a French word in pretty much every sentence makes it easier to understand, but it's hard to know which French word has been adapted officially, which has a Luxembourgish doublet, and which are only optionally thrown in for personal taste.
"Wou ass de Pierre? E gëtt malade sinn." (Where is Pierre? He got sick.)
"Monsieur, Dir hutt un d'Vacanz geduecht." (Sir, you thought about the vacation.)
This should get you started. Information taken from Assimil "Luxembourgeois de poche"