What is the ruling if hemorrhoid blood exits after completing ablution?
If this blood is exiting from outside the anus (due to the hemorrhoid protruding), it does not invalidate ablution, because blood exiting from the body from other than the two orifices does not invalidate ablution. If it exits from the anus (meaning from inside it), it invalidates ablution, and one must perform istinja' from it, wash the area of impurity, and repeat the ablution.
However, if this blood exits continuously such that no time remains sufficient for purification and prayer without it flowing, then it takes the ruling of urinary incontinence (sals al-bawl). One then cleanses from it after the time for each prayer enters, performs ablution immediately thereafter, and performs the obligatory prayer immediately. There is no liability upon him after that if something of it flows, and he may pray as many voluntary prayers as he wishes. If he wants to pray another obligatory prayer, he must cleanse himself and perform ablution. And Allah the Almighty knows best.
What is the ruling on reciting the takbīr from Sūrat aḍ-Ḍuḥā to Sūrat an-Nās upon completing the recitation of the Qur'an (khatm)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is recommended to recite the takbīr from the beginning of Sūrat aḍ-Ḍuḥā through to the end of Sūrat an-Nās, and this is the recitation practice of the people of Makkah.
It is stated in Nihāyat az-Zayn (p. 65): "It is sunnah to begin each sūrah with the basmalah, since it constitutes a verse of it. It is also sunnah to say, before each sūrah — from aḍ-Ḍuḥā to the end of the Qur'an — 'Lā ilāha illallāh, wallāhu akbar' (There is no god but Allah, and Allah is the Greatest), based on what has been narrated regarding Imam ash-Shāfi‘ī (raḍiyallāhu ‘anh), who heard a man reciting this takbīr in prayer, and said to him: 'You have done well, and you have hit upon the sunnah.'"
And Allah, the Exalted, knows best.
What is the ruling on congratulating others on the arrival of Ramadan?
Congratulating others on the arrival of Ramadan is permissible.
If someone does it to express their love for worship and the blessings of Ramadan, and congratulates their fellow Muslim, they have done something good.
The Prophet ﷺ said: "Shall I not tell you something that, if you do it, you will love one another? Spread peace (Salam) among yourselves." [Narrated by Muslim]
Giving Salam is a prayer for peace and safety.
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.