I guess there is no difference in meaning between الكراج بارد = the garage is cold and الكراج كراج بارد = the garage is a cold garage
Do you ever use the longer sentence and how? For example, just when you want to play with words, or does the longer sentence give a different emphasis?
It's for different use. Do you want to see an example? E.g. - How is the garage? - The garage is cold.
- All your house is so hot, there isn't any cold place in it, and in our house even the garage is hot.
- The garage is a cold garage.
It's true that you can say even in the second sentence, that simply just the garage is cold, but if you want to emphasize, you would use it like in the example sentence.
It seems that this course teaches Fusha/Modern Standard Arabic (only used on TV and newspapers and closest spoken dialect is Saudi and Khaliji/gulf arabic) which uses words like "doctor" and "garage" transliterated directly from English or French. I also study spoken arabic dialects, primarily shami/Levantine and masri/Egyptian. Some arabic dialects tend to use the words "mar'ab" for garage and "tabeeb" for doctor. Unfortunately other dialects use different words for garage and doctor so it is not standard from country to country.
In general, I believe Modern Standard Arabic tries to use the words and expressions that would be best understood from Northern to Southern and from Western to Eastern Arabic-Speaking Countries, or all the way from Morocco which speaks "Maghrebi" dialect to Yemen which speaks "Yemeni" dialect, and Syria "Levantine" dialect down to Sudan "Sudanese" dialect. This is a huge amount of space and if you do speak Fusha/Modern Standard Arabic to anyone they will be able to communicate with you in any arabic-dialect speaking country which is incredible. It is like saying one language allows you to communicate in all of Europe and Russia, where they actually speak like over 20 main languages.
It is good to pair this course with resources in Levantine or Egyptian dialect so you can also speak to people and they will immediately understand you as was the case for me when I speak Egyptian to any arabic speaker. I personally am learning both of these dialects so I can understand and communicate with as many speakers as possible.