Is it permissible to seek forgiveness (Istighfar) 10,000 times daily with the intention of fulfilling wishes within 7 days, or is that considered an innovation (bid‘ah)? And is it permissible to seek forgiveness for one's father and sister with the intention of having their needs fulfilled?

Seeking forgiveness (Istighfar) is a great act of worship that brings forth the good of this world and the religion. There is no text that specifies a certain number for it to achieve a specific matter within a set number of days. As for seeking forgiveness for one's parents and relatives, it is permissible because it is a form of supplication, as Allah Almighty says: "So be patient; indeed, the promise of Allah is truth. And ask forgiveness for your sin and exalt [Him] with praise of your Lord in the evening and the morning." There is no harm in having the intention of fulfilling their needs through it, for it is a form of seeking intercession with Allah through righteous deeds.