Is it permissible to pray at home, and is it accepted, especially given the hadith: "Whoever hears the call [to prayer] must respond to the prayer, except for one who has an excuse," and the saying of some that it is permissible because it is better than abandoning it altogether?

Congregational prayer is obligatory for free, adult men. Some scholars are of the opinion that it is obligatory to perform it in the mosque. Preserving it leads to great reward and avoids disagreement, so it should not be abandoned, as it holds great virtue.

If you pray in congregation at home, you have fulfilled the obligation and your responsibility is discharged. However, if you pray alone, your prayer is valid, though you incur sin. The statement of Sheikh al-Islam Ibn Taymiyyah regarding the invalidity of the prayer of one who neglects congregational prayer out of laxity is weak. The correct view is that congregational prayer is obligatory but not a condition for the validity of prayer. One who abandons it is sinful and disobedient.