Is it permissible to delay making up many missed prayers (for a year, for example) until the end of the day? Is there a sin in doing so, even if there is no preoccupation? Is it permissible to perform ablution at home beforehand for a missed prayer that will be made up later at work, especially with frequent flatulence?

The fundamental principle is to make up missed prayers immediately, to the best of one's ability. However, it is permissible to make up two or more days' worth of prayers in a single day. It is also permissible to limit oneself to making up one day's prayers per day if making up more would hinder one's efforts to earn a livelihood. There is no harm in delaying the making up of missed prayers until the end of the day if the questioner is busy with her sustenance, and it is not a condition to make them up immediately after ablution. She may pray them as long as her ablution has not been invalidated. As for a woman afflicted with chronic flatulence, she may pray as many prayers as she wishes with a single ablution within the prayer's time, and her ablution becomes invalid when the prayer time expires.