Must a person refrain from eating for the rest of the day if they break a fast of a vow (nadhr) or a make up fast (qada)?
Whoever observes a vowed fast (nadhr) or a makeup fast (qada) is prohibited from breaking it without a valid excuse. If they break it without a legitimate reason, they are sinful.
However, they are not required to refrain from eating for the rest of the day, because such restraint is only required out of respect for the month of Ramadan, not for other types of fasting.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?
All perfect praise be to Allah, The Lord of The Worlds. Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
What is the ruling on one who slept while firmly seated on the ground, regarding nullification of ablution?
The default ruling regarding sleep is that it nullifies ablution. An exception to this is one who slept while firmly seated on the ground; his ablution is not nullified by sleep if he wakes up while still firmly seated on the ground. And Allah the Almighty knows best.