Is a woman`s nephew by suckling considered a Mahram( i.e. unmarriageable)who is permitted to accompany her to Hajj?
All that is prohibited by lineage is prohibited by suckling, and a nephew by suckling is a Mahram like a nephew by lineage ;therefore, it is permissible for him to be a Mahram for his aunt in Hajj and Umrah.
What is the ruling on singing and listening to it while accompanied and unaccompanied by musical instruments?
Singing and listening to it unaccompanied by musical instruments is permissible as long as it isn`t practiced as a profession and is done by a man to other men, or a woman to other women with maintaining that no temptations are involved. The words of the song should be Islamic, and if temptation was likely to happen, then the singing becomes definitely forbidden. Temptation here means: whatever leads to committing a sin. In Islamic Sharia, singing accompanied by musical instruments such as the lute and the like is forbidden, and listening to it as well. The reason behind that is the fact that the musical instrument itself is forbidden. However, striking the tambourine and singing Islamic songs are permissible in weddings, circumcisions and the like.
What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?
One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days.
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.