Is there a virtue in dying during Ramadan? Is someone who dies a martyr if they pass away after remembering Allah, reciting the Shahada, and saying "Allahu Akbar," then fall into a coma and die? What is the ruling on hanging pictures of the deceased in the home for remembrance? Is someone who dies from an abdominal illness considered a martyr?

There is no specific virtue proven for dying in Ramadan (definition), unless the Muslim dies while fasting, due to the hadith (definition): "Whoever fasts one day seeking the Face of Allah, it will be sealed for him by entering Paradise."

Your father's coma after uttering the Shahada does not negate that the Shahada was his last words, unless he spoke after it. We hope that your father is among those included in the hadith: "Whoever's last words are 'La ilaha illa Allah' (There is no god but Allah) will enter Paradise."