Should the Fajr prayer be performed with the intention of timely performance (adaa’) or making up (qadaa’) when one wakes up late, not knowing the time of sunrise? Is it a condition for the worshiper to have the intention of timely performance or making up, and the intention of praying in congregation or individually?

Preserving the Fajr prayer at its appointed time and with the congregation holds immense virtue. Whoever prays it is under Allah's protection, as mentioned in the Hadith (definition), and becomes energetic and good-spirited. As for one who neglects it, he becomes lost and struggles with depression and distress. Regarding the intention for performing or making up a prayer, it is not a requirement. Similarly, the intention to pray alone is not required if one is praying by oneself. However, if one prays with a congregation, the intention to follow the Imam is necessary.