What is the ruling on intentionally delaying a prayer until its time has expired: does this constitute disbelief, and is his abandoning prayer without an excuse considered disbelief that necessitates not making it up? And is it obligatory to make up a prayer at home if one misses congregational prayer at the mosque without an excuse?

As for the disbelief of one who abandons prayer, there is a well-known difference of opinion concerning it, as there is concerning making up prayers intentionally missed. The majority opinion is that making them up is obligatory. Congregational prayer is obligatory according to the stronger opinion, but it is not a condition for the validity of the prayer according to the majority of scholars. Whoever abandons it sins, but their prayer is valid. The hadith "There is no prayer for him except with an excuse" is interpreted to mean the negation of a complete prayer. Congregational prayer is not a condition for the validity of the prayer according to Ahmad and others. Performing congregational prayer in the mosque is not obligatory according to most of those who deem congregational prayer obligatory; rather, wherever the individual performs it, their obligation is discharged.