Is it obligatory to have the intention for each day of fasting, or is one intention sufficient for the whole month?
The intention is obligatory for each day of Ramadan because each day is an independent act of worship separate from the others.
The intention must be made at night before the break of dawn, as the Prophetﷺ said: "Whoever does not intend fasting at night, there is no fast for him." [An-Nasa’i]
And he also said: "Whoever does not firmly resolve to fast before dawn, there is no fast for him." [At-Tirmidhi, Abu Dawood, and An-Nasa’i]
Whoever wakes up and eats Suhoor while mindful of fasting has made the intention. Likewise, one who firmly intends at any moment during the night to fast the next day has also fulfilled the intention.
Is it obligatory to make up all missed prayers?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Making up missed prayers (qaḍāʾ) is a sharʿī obligation, established by the practice of the Prophet ﷺ himself — when the disbelievers preoccupied him on the Day of the Trench and he missed the ʿAṣr prayer, he made it up afterward. This is further affirmed by the ḥadīth: "Fulfil what you owe to Allah, for Allah is most deserving of being fulfilled." (Reported by al-Bukhārī.)
Accordingly, a person who has missed prayers should set aside his voluntary and Sunnah prayers and replace them with make-up prayers in their stead. There is no objection to making up one missed prayer alongside each obligatory prayer that is performed — praying the equivalent missed prayer together with each current obligatory prayer as a practical and manageable way of gradually clearing one's debt of missed prayers. And Allah the Almighty knows best.
What is the ruling on having an intention (Niyyah) for every prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Intention (Niyyah) is a pillar (Rukn) without which the prayer is not valid. The worshiper must have an intention for every prayer, meaning they must consciously intend the act of worship they are performing. Its timing must coincide with the opening Takbir (Takbirat al-Ihram). It is not a requirement to utter it verbally; rather, doing so is considered a recommended Sunnah. There are three levels of intention:
1-If the prayer is obligatory (Fard): It is mandatory to include the Intent (to pray), the Specification (which prayer, e.g., 'Asr), and the Obligation (recognizing it as a Fard). For example, one should bring to mind or say: 'I intend to pray the Fard of 'Asr.'
2-If it is a voluntary prayer restricted by a specific time or cause (Sunnah Muqayyadah): It is mandatory to include the Intent and the Specification. For example: 'I intend to pray the Sunnah before Zuhr' or 'I intend to pray Duha.'
3-If it is an absolute voluntary prayer (Nafl Mutlaq): It is sufficient to simply have the Intent to pray. For example: 'I intend to pray.'
And Allah the Exalted knows best.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.