Duo uses some dialectal elements. I believe "qahwatuki" would be correct MSA.
Yes, in Standard (Arabic fuSa), it is:
هَذه قهوتُكِ يا سامِيةُ.
What is the difference between this is and this
This is your coffee
This coffee is yours
The sentence above is "This is your coffee". For it to be "This coffee is" the word coffee has to have the "al"
Correct, except you can't combine "al" with "your" as they're asking. So the example would be "This is your coffee", whereas "this coffee is yours" would be more along the lines of "هذه القهوة تبعك", "This coffee belongs to you"
The word تبعك is not used in fusha the equivalent would be لك / ملكك
هذه *قهوتُكِ. حركة كاف الخطاب للإناث تكون على الكاف نفسِه، ولا تكون على الحرف الذي قبل الكاف. رجاء الإنتباه.