What is the ruling on being excused by ignorance, and what are the limits of negligence in learning for someone who lives in a Muslim environment, but one that is heedless, and who later discovers past errors in their acts of worship?

As long as the questioner strives to correct her worship by seeking obligatory knowledge, there is no harm upon her. What she missed due to ignorance is excused, and she does not need to repeat it, because she grew up in a non-observant environment and relies on what she reads or hears of knowledge. Sheikh al-Islam Ibn Taymiyyah stated that whoever did not know the obligation, then upon learning it, should pray the current prayer and subsequent ones, and does not need to repeat previous ones, citing various incidents from the Sunnah as evidence. Ibn Uthaymeen said that a person is excused by ignorance in everything, as long as they were not negligent in seeking knowledge or arrogant after the evidence was conveyed to them.