yes .. it is a Tanwin or (-Un) sound following the "L" - I'm thinking they didn't put that diacritic sign for you here for simplicity maybe, not sure. Tanwin is like a sign for an indefinite noun. In full, the phrase above should be: رَجُلٌ سورِيْ - The mark over "L" (ل) is Tanwin bel Dham (-un)
Wy wouldn't there be offered first all new words in an english translation, like in other language learning sessions? That's like that now in this course from the beginning. In the other courses there are also being offered little pictures of the meaning (translation) of new words or phrases??
No. To have the definite article, you must add (AL) to the word: Al-Rajulu Al-Súriy (or more phonetically: Ar-rajulu-ssúriy). الرجل السوري
As you can see, adding the definite article to (man: رجل) would automatically add itself to the adjective (Syrian: سوري). Unless you are stating a fact: the man IS Syrian then the definite article is to be added only to the subject of the sentence: الرجل سوري (al-rajulu súriy).
Speaking in the "indefinite" sense, or in other words without introducing (AL) into the phrase or sentence, would require the placement of Tanwin or Nunation to the end of the noun (and its adjective). رجلٌ سوري (rajulun súriy) A Syrian man.
PS: The vowels on the last letter on the last word of a sentence or phrase can be dropped because, simply, the speech is over at this point and no profit is gained typically from adding the last vowel there.