Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
How can I love the prayer (Salah) and start praying?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Love for the prayer (Salah) comes when you realize that this world is fleeting and the Hereafter is everlasting. Your prayer is the righteous deed that will comfort you in your grave and be your salvation before Allah in the Hereafter. Do you not wish to attain tranquility in this life and Paradise in the next? Reflect upon your state and do not delay, for life does not wait. We ask Allah to grant us and you steadfastness (Thabat).
What is the amount of the Fitr Zakah (obligatory charity) of Ramadan?
The Fitr Zakah of Ramadhaan is a Sa` (2500 grams) from what the people of that country or state eat the most. And Allah Knows Best.
I read the Qudsī ḥadīth: "Whoever breaks his wuḍūʾ and does not perform ablution has shown me harshness; whoever performs ablution and does not pray has shown me harshness; whoever prays and does not supplicate to Me has shown me harshness; and whoever supplicates to Me and I do not answer him, then I have been harsh to him, and I am not a harsh Lord." What is the authenticity of this ḥadīth?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
This ḥadīth was mentioned by al-Ṣaghānī (may Allah have mercy on him) in al-Mawḍūʿāt (p. 43), where he said: “Among them is their saying: ‘Whoever breaks his wuḍūʾ and does not perform ablution has shown me harshness; whoever performs ablution and does not pray has shown me harshness; (whoever prays and does not supplicate to Me has shown me harshness); and whoever supplicates to Me and I do not answer him, then I have been harsh to him, and I am not a harsh Lord.’”
Al-ʿAjlūnī (may Allah have mercy on him) cited what al-Ṣaghānī said in Kashf al-Khafāʾ (Vol.2/p.264). And Allah Almighty knows best.