What should a sick person, who is incapable of fasting, and who didn`t make up for missed fasting days, do?
One who has missed fasting days is obliged to make up for them, but if he/she wasn`t able to because of an incurable disease , or old age, then he/she has to pay a ransom which is feeding a needy person for each of the missed fasting days.
What is the ruling on swearing a false oath by the Holy Quran?
Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.
Should vowed fast be offered in consecutive days, or not?
Vowed fast should be offered in line with what was originally intended by the vow-maker, either consecutively, or not.
Is it permissible for a woman to swear a false oath by the Holy Quran to please her distrustful husband?
It is forbidden for a person to do so since this is considered a false oath(Yamaan Ghamoos) which dips(Yaghmos) its taker in Hellfire if he/she doesn`t seek repentance, and he/she has to expiate for that oath. You should avoid any doubtful acts so that your husband`s chest remains clear from the evil suggestions of the devil.