Chautha is a ceremony that is conducted on the fourth day after the death.
Aap means "you" and is a respectful way to address a person as opposed to "tum" which is more casual. Older people are referred to by "aap" as an example.
Aaj means today.
ji is just another form of referring to somebody with respect. I can refer to you as Naomi-ji to show respect. Kind of like adding Sir or Ma'am to somebody's name but it does mean Sir or Ma'am.