Almost. You need to match the pronoun with the noun (in gender, number, case). When the adjective/pronoun/numeral precedes the noun that it further develops, then in majority of cases it has to agree with the noun in those 3 categories.
The pronoun "our" develops the noun "friend" (náš přítel). They must agree. You declined the masculine noun correctly in the genitive, singular and since the pronoun precedes, it will also be in the genitive, singular, masculine.
... syn našeho přítele/naší přítelkyně.
"Matěj is our friends son." is a valid translation (using Wordbank!) for "Matěj je syn našich přátel." All I get is "You are correct". I am used to get at least a corrective spelling when I miss apostrophes etc. Or can the apostrophe be omitted in modern English nowadays or is it sometimes added but not displayed ? But why is neither an "of" nor "friends' " in the wordbank?
the apostrophe definitely matters! i got it wrong because i wrote "friend's" which is belonging to a singular friend, instead of the plural possessive "friends'." the wordbank is sometimes wrong. for a lot of the last lesson there was a normal "d" when it should have said "d'." i prefer to use the desktop version and type instead of use the wordbank. i think it's more conducive to learning that way as well. hopefully the mobile version improves with time :).
Although the grammar notes nicely asked us to not translate Czech proper names, I have found an inconsistency. Mostly I have pasted the names in, but I tried typing them without accents. Keterina was accepted but not Matej. Properly transcribed into English, all proper names in general lose their accents. However I guess this rule is not always followed. Actually I am not too bothered. I can put in the accents. But I did find the inconsistency.
Yes, přítel nom. sg., přátel is gen. pl., see https://en.wiktionary.org/wiki/p%C5%99%C3%ADtel#Declension
You just have to learn it, there are more words with irregular plural genitives at http://prirucka.ujc.cas.cz/?id=227