The MSA for my bag is حَقيبَتي
The one used here "شَنطَتي" is used in the Egyptian dialect and maybe others I'm not aware of.
The gender of the words does not change by the gender of the speaker. Both words, Coffee قهوة and Bag شنطة (which is wrong by the way) are feminine.
The proper word for "bag" in Arabic is حقيبة (Haqíbah). The word شنطة (šanTa) is originally from Turkish (çanta) and it is used in some dialects. But it's NOT a standard Arabic word.
No, they are both feminine.
The 2 options in the problem are asking how you spell قهوة Qahwa when it's put in the possessive "my coffee".
The answer is the "tied tah" tah marbuta ة is "untied" and both spelled and pronounced as a "tah" ت
So the spelling converts to قهوتي not قهوةي. It is pronounced Qahwatii. But it's just a re-spelling of the tah marbuta, not changing the gender.