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.
That is a brilliant answer to the question. I think we might have got the answer right, just after we were taught that tah marbuta is unfurled into explicit a-t before a case ending. But now that we've been taught that in the possessive construction the tah marbuta is untied in the pronunciation but not in the spelling, our brain, well at least, my brain, has turned to porridge and wanted to keep the tah marbutted so to speak.