In most cases it is really simple:
You are almost NEVER forced to use any other grammar but German grammar when terms from foreign countries are embedded in German sentences. Otherwise you had to learn the grammar from every language of the world to build proper german sentences including foreign terms.
A few examples:
The word "Kimono" is from Japanese language. In a german sentence you can build the plural or the accusative of it without learning Japanese: "In meinem Schrank hängen zwei Kimonos. Ich habe den Kimono zur Wäsche gegeben."
The word "Safari" is from Suaheli language. You can build correct german sentences with this word without any knowledge of Suaheli: "Franz will an einer Safari teilnehmen."
"Hobby" and "Baby" are english words. So in German sentences you have to decline them according to German rules: "Anna hat zwei Babys (NOT Babies!!) bekommen. Eines ihrer Hobbys (NOT Hobbies!!) ist Stricken."
... there are some exceptions for latin words.
Der Leib Christi (not "der Leib Christus"). (latin: "corpus christi")
In Salzburg und Wien stehen zwei berühmte Collegia musica (not Collegiums musicum)
Declination of latin words in german sentences is tricky. Sometimes you have to use German grammar and sometimes Latin Grammar. It is really hard to tell when you have to use which grammar. The best way is to do what german native speakers do: Look it up in a dictionary. In doubt use German grammar.
A famous example:
The latin plural of the word "status" is "status" (the rule is named "u-declination") and in German you can use "die Status" as plural of "der Status" ("Vier verschiedene Status können einen Alarm auslösen"). But there are more latin words ending with "-us" who's plural ends with "-i" (dominus - domini). Since only few german speaking people know latin grammar many of them tend to build the wrong plural "Stati" ("Vier verschiedene Stati ..."). They would have done better if they had used german grammar ("Vier verschiedene Statusse ...") because "Statusse" is also a correct variation of the plural of "Status".