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 of Islamic Law if the follower (maʾmūm) stands up for the third rakʿah out of forgetfulness while the imam has sat for the middle tashahhud?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If the imam sits for the tashahhud while the follower (maʾmūm), out of forgetfulness, stands up for the third rakʿah, he is obliged to return to his sitting position, since following the imam is obligatory. In this case, no prostration of forgetfulness (sujūd al-sahw) is required of him. If, however, he fails to return, his prayer is rendered invalid.
Shaykh al-Islām Imām Zakariyyā al-Anṣārī, may Allah have mercy upon him, states: "If the follower stands up alone out of forgetfulness, he is obliged to return, since following the imam is obligatory... If he does not return, his prayer is rendered invalid, due to his departure from what is obligatory." [Asnā al-Maṭālib,Vol.1/P.190] And Allah the Almighty knows best.
Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.