What should I do if the doorbell rings while I am praying and there is no one else in the house, and am I sinful if I interrupt my prayer?

It is permissible to interrupt a supererogatory (nafila) prayer when there is a need to know who is at the door, whereas it is not permissible to interrupt an obligatory (fard) prayer except for an important necessity that is feared to be missed. It is preferred for men to alert others by saying "Subhan Allah" (Tasbeeh) and for women to clap to indicate that they are engaged in prayer, based on the Prophet's (peace be upon him) saying: "Whoever experiences something during their prayer, let men say 'Subhan Allah' and women clap." If that does not work, it is permissible to interrupt the supererogatory prayer out of need. As for the obligatory prayer, it is interrupted only for a pressing necessity and must be restarted from the beginning.